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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

The Marriage of Residential Energy Codes and Rating Systems: Conflict Resolution or Just Conflict?

After three decades of coexistence at a distance, model residential energy codes and residential energy rating systems have come together in the 2015 International Energy Conservation Code. At the October, 2013, International Code Council’s Public Comment Hearing, a new compliance path based on an Energy Rating Index was added to the IECC. Although not specifically named in the code, RESNET’s HERS rating system is the likely candidate Index for most jurisdictions. While HERS has been a mainstay in various beyond-code programs for many years, its direct incorporation into the most popular model energy code raises questions about the equivalence of a HERS-based compliance path and the traditional IECC performance compliance path, especially because the two approaches use different efficiency metrics, are governed by different simulation rules, and have different scopes with regard to energy impacting house features. A detailed simulation analysis of more than 15,000 house configurations reveals a very large range of HERS Index values that achieve equivalence with the IECC’s performance path. This paper summarizes the results of that analysis and evaluates those results against the specific Energy Rating Index values required by the 2015 IECC. Based on the home characteristics most likely to result in disparities between HERS-based compliance and performance path compliance, potential impacts on the compliance process, state and local adoption of the new code, energy efficiency in the next generation of homes subject to this new code, and future evolution of model code formats are discussed.

Residential, Energy, Rating systems, HERS, 2015 IE↗
DOE OSTI2019

Benchmark Study on Innovative Fuels for Fast Reactors with fuel performance codes

The Working Party on the Scientific Issues of the Fuel Cycle (WPFC) has been established under the auspices of the Nuclear Energy Agency (NEA) Nuclear Science Committee (NSC), to co-ordinate scientific activities regarding various existing and advanced nuclear fuel cycles, including advanced reactor systems, associated chemistry and flowsheets, development and performance of fuels and materials, accelerators and spallation targets. Various expert groups were established to cover the above-mentioned topics. Within the WPFC, the Expert Group on Innovative Fuels (EGIF) was created with the objective of conducting joint and comparative studies to support the development of innovative fuels such as homogeneous and heterogeneous fuels, ADS fuels, and oxide, metal, nitride and carbide fuels, all of which can be implemented in advanced nuclear fuel cycles with fast reactors. The scope of the expert group covers innovative fuel fabrication techniques, irradiation performance of innovative fuels, characterisation and post-irradiation examination methods and predictive codes for innovative fuel fabrication and performance. This report presents the results of a benchmark study on innovative fuels for fast reactors using fuel performance codes. Irradiation results were shared among participants, and code calculations were performed to gain further insights on the fuel behaviour. Each participating institution used its own fuel performance code. Code to code and code to experiment comparisons are expected to provide data and improve understanding on the effects of minor actinides on fuel behaviour. In conclusion, the need for improvement of codes will be evaluated and the needs for new experimental data will be identified in order to finalise the code validation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2016

Full Integration of the Fission Product Release Module STACY into the HTR Code Package (HCP) - 18661

The HTR Code Package is under development since 2010 at Forschungszentrum Juelich and at Aachen University. The HCP combines the capabilities of individual legacy codes developed during the German HTR program in a highly integrated manner and contains new features. Within the HCP, all aspects related to fission product release and the redistribution within the primary circuit are handled by the module STACY (Source Term Analysis Code system). STACY is the successor of the codes FRESCO-I/II (dealing with fission product release) and PANAMA (dealing with fuel performance issues). Compared to these predecessor codes, STACY can take amongst others a time-dependent nuclide inventory and a radial temperature profile within the fuel element into account. So far, this version of STACY performs an individual fission product release calculation for a representative number of tracer pebbles. While this version of STACY still relies on codes like VSOP and MGT-3D and contains features such as basic fuel management which are also contained in the before mentioned codes, STACY now will be coupled to forms an integral part of the HCP. Thus, fission product release calculations will be examined with one consistent reactor input model. This allows assessing the release of fission products already during the design phase, besides parameters like the maximum fuel temperature during a transient. Furthermore the total nuclide inventory of a fuel element is distributed among fuel kernels, coating layers, graphite grains and pores of the surrounding matrix graphite. Formerly, this total inventory calculated by the burnup code TNT was distributed according to the distribution of Uranium. As a new feature, STACY now keeps track of the distributions of nuclide inventories within the fuel element. Especially for nuclides mainly formed by activation and decay processes like Ag-110m, this approach is more accurate. Further, the knowledge about the actual nuclide inventories improves the accuracy of fuel performance calculations. In addition, the internal coupling allows a feedback from the fission product calculation to other code modules. Nuclides amounts being released can be considered in e.g. the burnup calculation while calculating the source term of for example tritium or within the calculation which takes care of the redistribution of species by the coolant. Within this paper, the application of the STACY to HTR cores with special emphasis on fission product release to reactor models such as the HTR-Modul and HTR-10 will be discussed. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2014

A Code of Radiation Damage by Gamma - Paper 62

In recent years, the study of radiation damage of materials has seen a thrust because of the expectation of the high rate of radiation damage in fusion reactors, accelerator driven sub critical systems and damage of a control system of space vehicles by the high energy neutrons and gamma showers. Embrittlement of reactor vessels, corrosion of steel and swelling of fuel rods are the well known empirical examples of severe radiation damage. It is also realized that damage by high energy gammas is in no way insignificant, and it is equivalent to the damage by the neutrons. Secondly, value addition of certain materials like enhancement of electrical resistance, mechanical strength, color enhancement of precious stones on irradiation by neutrons and gammas and polymerization in the presence of gamma radiation add to the necessity of a Monte Carlo (MC) code of radiation damage in a wide range of energy. The JAIPU code, for the study of radiation damage by neutrons up to 10 MeV energy, incorporates features like development of secondary atomic cascade and PKA energy corrected for the ionization lose and production of Frenkel pair. MC estimation of both the primary and secondary displacements has been compared with the Frenkel pairs calculated using the NRT model. In the present work, JAIPU code is extended for irradiation of materials by high energy gammas. Here cascade generated by the incident gamma produces electrons by way of photo-electric, Compton and pair production until it is absorbed. The recoiled Frenkel pairs produced in electron + atom collision have been considered for the purpose of atomic cascade. Standard cross section libraries for gamma and electron interaction are used while for atom + atom collision we have made use of the IOTA code. In addition, in the code, the lattice structure of the irradiated material is simulated to know the positions of the photon interactions with atoms and the energy of electron it adds an extra feature of the position and size of the voids and the clusters produced on irradiation. The code has the possibility of calculation of 'absorbed radiation dose' and 'KERMA' and the interatomic distances of the displaced atoms. It may be pointed out that the code uses only the MC simulation of the number of displacements unlike several other approaches where the NRT model with PKA energy is used for gross estimation of the number of the displaced atoms. Thus, the code keeps an account of the positions of displaced atoms for the in-depth modification of the irradiated material. 1 MeV gamma seems to damage Fe up to several millimeters of its depth and this is mostly by the recoiled Compton electrons than photo electrons. The code is in the developmental stage and it has the capability of applications in the developing field of Radiology besides the shielding and other studies of radiation damage. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Coupling TRACE with nodal neutronics code Ants using the Exterior Communications Interface and VTT's multi-physics driver Cerberus

In this paper a recently developed coupling between system code TRACE and nodal neutronics code Ants is presented. The TRAC/RELAP Advanced Computational Engine (TRACE) is a reactor system code developed by U.S. Nuclear Regulatory Commission (NRC). The code has been designed to analyse loss-of-coolant accidents (LOCAs), operational transients and other accident scenarios in light water reactors. Ants is the reduced order nodal neutronics code of the Kraken framework. The diffusion solution method in Ants is based on the Analytic Function Expansion Nodal method (AFEN) and Flux Expansion Nodal Method (FENM). Rectangular, hexagonal and triangular geometries are supported. Both steady state and burnup problems including micro-depletion can be simulated. The coupling is implemented using VTT's multi-physics driver Cerberus and the Exterior Communications Interface (ECI) which is supplied with TRACE and enables the coupling of TRACE without source code modifications. The main focus in the paper is on describing the TRACE-Ants coupling in detail in order to share to other code developers what we have learned from the ECI based coupling process. The coupled code system is briefly tested by simulating a simple transient in a SMR core initiated by control rod movement. The results of the test calculation look reasonable and more complicated test cases will be modelled in the near future.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2013

NSDann2BS, a neutron spectrum unfolding code based on neural networks technology and two bonner spheres

In this work a neutron spectrum unfolding code, based on artificial intelligence technology is presented. The code called ''Neutron Spectrometry and Dosimetry with Artificial Neural Networks and two Bonner spheres'', (NSDann2BS), was designed in a graphical user interface under the LabVIEW programming environment. The main features of this code are to use an embedded artificial neural network architecture optimized with the ''Robust design of artificial neural networks methodology'' and to use two Bonner spheres as the only piece of information. In order to build the code here presented, once the net topology was optimized and properly trained, knowledge stored at synaptic weights was extracted and using a graphical framework build on the LabVIEW programming environment, the NSDann2BS code was designed. This code is friendly, intuitive and easy to use for the end user. The code is freely available upon request to authors. To demonstrate the use of the neural net embedded in the NSDann2BS code, the rate counts of {sup 252}Cf, {sup 241}AmBe and {sup 239}PuBe neutron sources measured with a Bonner spheres system.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

TWANG-PIC, a novel gyro-averaged one-dimensional particle-in-cell code for interpretation of gyrotron experiments

A new gyrotron simulation code for simulating the beam-wave interaction using a monomode time-dependent self-consistent model is presented. The new code TWANG-PIC is derived from the trajectory-based code TWANG by describing the electron motion in a gyro-averaged one-dimensional Particle-In-Cell (PIC) approach. In comparison to common PIC-codes, it is distinguished by its computation speed, which makes its use in parameter scans and in experiment interpretation possible. A benchmark of the new code is presented as well as a comparative study between the two codes. This study shows that the inclusion of a time-dependence in the electron equations, as it is the case in the PIC-approach, is mandatory for simulating any kind of non-stationary oscillations in gyrotrons. Finally, the new code is compared with experimental results and some implications of the violated model assumptions in the TWANG code are disclosed for a gyrotron experiment in which non-stationary regimes have been observed and for a critical case that is of interest in high power gyrotron development.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Geometric Structure and Transversal Logic of Quantum Reed–Muller Codes

Designing efficient and noise-tolerant quantum computation protocols generally begins with an understanding of quantum error-correcting codes and their native logical operations. The simplest class of native operations are transversal gates, which are naturally fault-tolerant. Here, in this paper, we aim to characterize the transversal gates of quantum Reed–Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. We start our work by establishing a new geometric characterization of quantum RM codes via the Boolean hypercube and its associated subcube complex. More specifically, a set of stabilizer generators for a quantum RM code can be described via transversal X and Z operators acting on subcubes of particular dimensions. This characterization leads us to define subcube operators composed of single-qubit π/2 k Z -rotations that act on subcubes of given dimensions. We first characterize the action of subcube operators on the code space: depending on the dimension of the subcube, these operators either (1) act as a logical identity on the code space, (2) implement non-trivial logic, or (3) rotate a state away from the code space. Second, and more remarkably, we uncover that the logic implemented by these operators corresponds to circuits of multi-controlled-Z gates that have an explicit and simple combinatorial description. Overall, this suite of results yields a comprehensive understanding of a class of natural transversal operators for quantum RM codes.

Reed–Muller (RM) codes↗
DOE OSTI2026

Performance-Aligned LLMs for Generating Fast HPC Code

Optimizing scientific software is a difficult task because codebases are often large and complex, and performance can depend upon several factors including the algorithm, its implementation, and hardware among others. Causes of poor performance can originate from disparate sources and be difficult to diagnose. Recent years have seen a multitude of work that use large language models (LLMs) to assist in software development tasks. However, these tools are trained to model the distribution of code as text, and are not specifically designed to understand performance aspects of code. In this work, we introduce a reinforcement learning based methodology to align the outputs of code LLMs with performance. This allows us to build upon the current code modeling capabilities of LLMs and extend them to generate better performing code. Here, we demonstrate that our fine-tuned model improves the expected speedup of generated code over base models for a set of benchmark tasks from 0.9 to 1.6 for serial code and 1.9 to 4.5 for OpenMP parallel code.

Computer science↗
DOE OSTI2013

Steady-State Gyrokinetics Transport Code (SSGKT), A Scientific Application Partnership with the Framework Application for Core-Edge Transport Simulations, Final Report

This project initiated the development of TGYRO - a steady-state Gyrokinetic transport code (SSGKT) that integrates micro-scale GYRO turbulence simulations into a framework for practical multi-scale simulation of conventional tokamaks as well as future reactors. Using a lightweight master transport code, multiple independent (each massively parallel) gyrokinetic simulations are coordinated. The capability to evolve profiles using the TGLF model was also added to TGYRO and represents a more typical use-case for TGYRO. The goal of the project was to develop a steady-state Gyrokinetic transport code (SSGKT) that integrates micro-scale gyrokinetic turbulence simulations into a framework for practical multi-scale simulation of a burning plasma core ? the International Thermonuclear Experimental Reactor (ITER) in particular. This multi-scale simulation capability will be used to predict the performance (the fusion energy gain, Q) given the H-mode pedestal temperature and density. At present, projections of this type rely on transport models like GLF23, which are based on rather approximate fits to the results of linear and nonlinear simulations. Our goal is to make these performance projections with precise nonlinear gyrokinetic simulations. The method of approach is to use a lightweight master transport code to coordinate multiple independent (each massively parallel) gyrokinetic simulations using the GYRO code. This project targets the practical multi-scale simulation of a reactor core plasma in order to predict the core temperature and density profiles given the H-mode pedestal temperature and density. A master transport code will provide feedback to O(16) independent gyrokinetic simulations (each massively parallel). A successful feedback scheme offers a novel approach to predictive modeling of an important national and international problem. Success in this area of fusion simulations will allow US scientists to direct the research path of ITER over the next two decades. The design of an efficient feedback algorithm is a serious numerical challenge. Although the power source and transport balance coding in the master are standard, it is nontrivial to design a feedback loop that can cope with outputs that are both intermittent and extremely expensive. A prototypical feedback scheme has already been successfully demonstrated for a single global GYRO simulation, although the robustness and efficiency are likely far from optimal. Once the transport feedback scheme is perfected, it could, in principle, be embedded into any of the more elaborate transport codes (ONETWO, TRANSP, and CORSICA), or adopted by other FSP-related multi-scale projects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Electric Vehicle Charging for Residential and Commercial Energy Codes: Technical Brief

Numerous studies show that sales of electric vehicles (EVs) have grown consistently over recent years in the U.S. The U.S. Energy Information Administration (EIA) estimated 3 million EVs were on the road in 2022, and the Edison Electric Institute (EEI) forecasts a total of 26.4 million EVs on the road by 2030. Based on this forecast, EEI projects the need for an additional 12.9 million EV charge ports by 2030. If EV charging infrastructure fails to keep pace with sales of EVs it could result in consumers stranded without options to power their vehicles. EVs are capable of providing substantial benefits to the consumers. EVs are less expensive to operate than conventional internal combustion engine vehicles, have lower maintenance costs, and have the convenience of fueling (charging) at home or work. Studies conducted in California show that costs associated with installing EV charging infrastructure can be substantially more expensive for retrofit scenarios compared to new construction, making inclusion of EV infrastructure in new construction codes a cost-effective policy option to increase infrastructure to meet growing demands. PNNL tracks adoption of mandatory EV provisions across the U.S. As of December 20, 2024, 12 states (California, Oregon, Washington, Colorado, New Mexico, Illinois, Maryland, Delaware, New Jersey, Rhode Island, Massachusetts and Vermont) and 53 local governments have added EV provisions to their building codes, local ordinances and zoning requirements. Originally published in 2022, this tech brief has been revised to align with recent model energy code committee discussions and published EV infrastructure code language. This technical brief summarizes market trends, costs and benefits, and provides sample code language for EV charging infrastructure for consideration to be included in model codes, such as the International Energy Conservation Code (IECC) and ANSI/ASHRAE/IES Standard 90.1, as well as directly by states and local governments in their building codes. The technical brief summarizes related efforts undertaken by states and local governments, and builds upon language considered during the 2021 and 2024 IECC development cycles.

2021 IECC↗
DOE OSTI2016

Modified versions of the fuel performance codes RTOP and RTOP-CA

RTOP code predicts thermal and mechanical behavior of LWR fuel rods and release of GFPs both in normal stationary and transient operation modes, and transient power ramps, specific to the reactivity-initiated accidents (RIA). Computational domains of the code include fuel column, zirconium cladding, gas under cladding, and fuel microstructure - UO{sub 2} grain and the development of gaseous porosity of different origin during irradiation. RTOP-CA code is based on the RTOP code. It simulates the behavior of a fuel rod with cladding rupture opening and RFPs release into the primary coolant circuit in normal operation modes. The paper presents the results of development and validation of engineering models, which take into account characteristics of the neutron spectrum during the fuel cycle and are integrated into modernized versions of the fuel performance codes RTOP and RTOP-CA. The paper focuses on the detailed description of two models. Four-group neutron-physical engineering model describes burn-out of gadolinium isotopes and calculates spatial power profile in a Gd-doped fuel rod pellet. The second engineering model presented is developed for fast estimation of fuel burnup in case of fuel rod cladding leakage accident. The comparison of the present calculations with the results of calculations by neutron codes shows that the model describes the heat rate distribution and the gadolinium burn-out with sufficient accuracy. The code also calculates the LHR of Gd-doped fuel rods given the heat rate of the adjacent UO{sub 2} fuel rods. This work allows determining the histories of LHR for the Gd-doped fuel rod from the average LHR of FA for various equilibrium WWER fuel cycles, power units and fuel enrichments. The presented model is implemented in the RTOP fuel performance code to calculate the thermomechanical behavior of the fuel rods. An engineering-physical model is developed for fast estimation of {sup 134}Cs/{sup 137}Cs activity ratio in fuel taking into account the parameters of the neutron spectrum during the fuel cycle. Implementation of the model enables to increase the reliability of correct fuel burnup determination in a failed fuel assembly (FA)based on the FERDS activity measurements during reactor operation. Results of the model calculations obtained for the FAs with a higher fuel enrichment and the NPP activity measurements have shown a higher {sup 134}Cs/{sup 137}Cs activity ratio compared to the values for the fuel with enrichment up to 3.6 wt. % in {sup 235}U. Currently, the engineering model is applicable within the range of UO{sub 2} enrichment from 3 to 5 wt. % in {sup 235}U, and Gd{sub 2}O{sub 3} enrichment from 5 to 8 wt. %.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Efficient Binary Static Code Data Flow Analysis Using Unsupervised Learning

The ever increasing need to ensure that code is reliably, efficiently and safely constructed has fueled the evolution of popular static binary code analysis tools. In identifying potential coding flaws in binaries, tools such as IDA Pro are used to disassemble the binaries into an opcode/assembly language format in support of manual static code analysis. Because of the highly manual and resource intensive nature involved with analyzing large binaries, the probability of overlooking potential coding irregularities and inefficiencies is quite high. In this paper, a light-weight data, unsupervised data flow methodology is described which uses highly-correlated data flow graph (CDFGs) to identify coding irregularities such that analysis time and required computing resources are minimized. Such analysis accuracy and efficiency gains are achieved by using a combination of graph analysis and unsupervised machine learning techniques which allows an analyst to focus on the most statistically significant flow patterns while performing binary static code analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

An efficient SAC-OCDMA system using three different codes with two different detection techniques for maximum allowable users

In this paper, three codes spectral amplitude coding optical code division multiple access (SAC-OCDMA) are proposed and compared in terms of system performance including bit error rate (BER), number of active users, high achievable data rate, high signal to noise ratio (SNR) and the minimum received power that the OCDMA system supports to achieve a minimum BER value. The proposed codes are diagonal double weight (DDW) codes, modified double weight (MDW) codes and enhanced double weight (EDW). Different detection as AND subtraction detection technique and single photodiode detection (SPD) are investigated to reduce the effect of both the multiple access interference and phase induced intensity noise. The obtained results show that SAC-OCDMA using EDW code with SPD detection can achieve large number users with better BER (~ 10{sup −9}), SNR (> 20 dB), and minimum received power (~ − 20 dBm) relative to the other codes with other detection techniques.

42 ENGINEERING↗
DOE OSTI2018

Performance analysis and implementation details of the Energy Conserving Semi-Implicit Method code (ECsim)

We present in this work the implementation of the Energy Conserving Semi-Implicit Method in a parallel code called ECsim. This new code is a three-dimensional, fully electromagnetic particle in cell (PIC) code. It is written in C/C++ and uses MPI to allow massive parallelization. ECsim is unconditionally stable in time, eliminates the finite grid instability, and has the same cycle scheme as the explicit code with a computational cost comparable to other semi-implicit PIC codes. All these features make it a very valuable tool to address situations which have not been possible to analyze until now with other PIC codes. In this work, we show the details of the algorithm implementation and we study its performance in different systems. ECsim is compared with another semi-implicit PIC code with different time and spectral resolution, showing its ability to address situations where other codes fail.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Distributing User Code with the CernVM FileSystem

The CernVM FileSystem (CVMFS) is widely used in High Throughput Computing to efficiently distributed experiment code. However, the standard CVMFS publishing tools are designed for a small group of people from each experiment to maintain common software, and the tools are not a good fit for publishing software from numerous users in each experiment. As a result, most user code, such as code to do specific physics analyses, is still sent with every job to the place the job is run. That process is relatively inefficient, especially when the user code is large. To overcome these limitations, we have built a CVMFS user code publication system. This publication system enables users to still submit their code with their jobs but the code is distributed and accessed through the standard CVMFS infrastructure. The user code is automatically deleted from CVMFS after a period of no use. Most of the software for the system is available as a single self-contained open source rpm called cvmfs-user-pub and is available for other deployments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Low-Density Parity-Check Codes as Stable Phases of Quantum Matter

Phases of matter with robust ground-state degeneracy, such as the quantum toric code, are known to be capable of robust quantum information storage. Here, we address the converse question: given a quantum error-correcting code, when does it define a stable gapped quantum phase of matter, whose ground-state degeneracy is robust against perturbations in the thermodynamic limit? We prove that a low-density parity-check (LDPC) code defines such a phase, robust against all few-body perturbations, if its code distance grows at least logarithmically in the number of degrees of freedom, and it exhibits “check soundness.” Many constant-rate quantum LDPC expander codes have such properties, and define stable phases of matter with a constant zero-temperature entropy density, violating the third law of thermodynamics. Our results also show that quantum toric-code phases are robust to spatially nonlocal few-body perturbations. Similarly, phases of matter defined by classical codes are stable against symmetric perturbations. In the classical setting, we present improved locality bounds on the quasiadiabatic evolution operator between two nearby states in the same code phase.

quantum error correction↗
DOE OSTI2025

Low-Density Parity-Check Stabilizer Codes as Gapped Quantum Phases: Stability under Graph-Local Perturbations

We generalize the proof of stability of topological order, due to Bravyi, Hastings, and Michalakis, to stabilizer Hamiltonians corresponding to low-density parity-check (LDPC) codes without the restriction of geometric locality in Euclidean space. We consider Hamiltonians 𝐻 0 defined by ⟦𝑁,𝐾,𝑑⟧ LDPC codes, which obey certain topological quantum order conditions: (i) code distance 𝑑 ≥ 𝑐⁢log (𝑁), implying local indistinguishability of ground states, and (ii) a mild condition on local and global compatibility of ground states—these include good quantum LDPC codes and the toric code on a hyperbolic lattice, among others. We consider stability under weak perturbations that are quasilocal on the interaction graph defined by 𝐻 0 and that can be represented as sums of bounded-norm terms. As long as the local perturbation strength is smaller than a finite constant, we show that the perturbed Hamiltonian has well-defined spectral bands originating from the 𝑂⁡(1) smallest eigenvalues of 𝐻 0 . The band originating from the smallest eigenvalue has 2 𝐾 states, is separated from the rest of the spectrum by a finite energy gap, and has exponentially narrow bandwidth 𝛿 =𝐶⁢𝑁⁢𝑒 −Θ⁡(𝑑) , which is tighter than the best-known bounds even in the Euclidean case. We also obtain that the new ground-state subspace is related to the initial-code subspace by a quasilocal unitary, allowing one to relate their physical properties. Our proof uses an iterative procedure that performs successive rotations to eliminate non-frustration-free terms in the Hamiltonian. Our results extend to quantum Hamiltonians built from classical LDPC codes, which give rise to stable symmetry-breaking phases. These results show that LDPC codes very generally define stable gapped quantum phases, even in the non-Euclidean setting, initiating a systematic study of such phases of matter.

mathematical physics↗