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Results for “density matrix renormalization”
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Ground-state order in magic-angle graphene at filling ν = - 3 : A full-scale density matrix renormalization group study
Here we investigate twisted bilayer graphene (TBG) at filling ν = -3 in the presence of realistic heterostrain. Strain amplifies the band dispersion and drives the system beyond the strong-coupling regime of previous theoretical studies. We use DMRG to conduct an unbiased, large-scale numerical calculations that include all spin and valley degrees of freedom, up to bond dimension χ = 24576. We establish a global phase diagram that unifies a number of theoretical and experimental results. Near zero strain we find an intervalley-coherent quantized anomalous Hall (QAH-IVC) state, a competitive strong-coupling order that evaded past numerical studies. A tiny strain around 0.05% drives a transition into an incommensurate Kekulé spiral (IKS) phase, supporting the mean-field prediction in [Kwan, Phys. Rev. X 11, 041063 (2021)2160-330810.1103/PhysRevX.11.041063]. Even higher strains above 0.2% favor a flavor-symmetric metallic order, which may explain metals found at ν = -3 in many experiments.
Two-dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method
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Renormalized density matrix downfolding: A rigorous framework in learning emergent models from ab initio many-body calculations
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Chiral Spin Liquid Phase of the Triangular Lattice Hubbard Model: A Density Matrix Renormalization Group Study
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Strongly anisotropic electronic and magnetic structures in oxide dichlorides RuOCl 2 and OsOCl 2
The van der Waals oxide dichlorides MOX 2 (M=V, Ta, Nb, Ru, and Os; X=halogen element), with different electronic densities, are attracting considerable attention. Ferroelectricity, spin-singlet formation, and orbital-selective Peierls phases were reported in this family with d 1 or d 2 electronic configurations, all believed to be caused by the strongly anisotropic electronic orbital degree of freedom. Here, using density functional theory and density matrix renormalization group methods, we investigate the electronic and magnetic properties of RuOCl 2 and OsOCl 2 with d 4 electronic configurations. Different from a previous study using VOI 2 with d 1 configuration, these systems with 4d4 or 5d4 do not exhibit a ferroelectric instability along the a axis. Due to the fully occupied dxy orbital in RuOCl 2 and OsOCl 2 , the Peierls instability distortion disappears along the b axis, leading to an undistorted Immm phase (No. 71). Furthermore, we observe strongly anisotropic electronic and magnetic structures along the a axis. For this reason, the materials of our focus can be regarded as “effective one-dimensional” systems even when they apparently have a dominant two-dimensional lattice geometry. The large crystal-field splitting energy (between dxz/yz and dxy orbitals) and large hopping between nearest-neighbor Ru and Os atoms suppresses the J = 0 singlet state in MOCl 2 (M=Ru or Os) with electronic density n = 4, resulting in a spin-1 system. Moreover, we find staggered antiferromagnetic order with π wave vector along the M-O chain direction (a axis) while the magnetic coupling along the b axis is weak. Based on Wannier functions from first-principles calculations, we calculated the relevant hopping amplitudes and crystal-field splitting energies of the t 2g orbitals for the Os atoms to construct a multiorbital Hubbard model for the M-O chains. Staggered AFM with ↑|-|↓-↑|-|↓ spin structure dominates in our density matrix renormalization group calculations, in agreement with density functional theory calculations. Our results for RuOCl 2 and OsOCl 2 provide guidance to experimentalists and theorists working on this interesting family of oxide dichlorides.
A numerically exact description of ultrafast vibrational decoherence in vibration-coupled electron transfer
Broadband pump–probe spectroscopy has been widely used to measure vibrational decoherence associated with the reaction coordinate in photoinduced ultrafast vibration-coupled electron transfer (VCET) reactions. These experiments provide insight into the interplay of intramolecular coordinates along the reaction coordinate. However, a general theoretical foundation for analyzing, and even for explaining rigorously, these data is lacking. In this work, we study vibrational decoherence in a model VCET reaction using the nearly exact time-dependent density matrix renormalization group simulation method. We explore how analyzing the density matrix with quantum information measures can help elucidate the evolution of vibrational coherence in simulations of dynamics. We examine how vibrational coherence is affected by electron transfer on the timescale of approximately 100 femtoseconds. Our results suggest that electron transfer, in the nonadiabatic model, changes the vibrational equilibrium position abruptly—an example of a “quantum quench” event. This explains the concomitant vibrational decoherence. We find that abrupt vibrational decoherence can be mitigated by wavepacket motion occurring on the timescale of the electron transfer.
Emergent Superconductivity and Competing Charge Orders in Hole-Doped Square-Lattice t – J Model
The square-lattice Hubbard and closely related t-J models are considered as basic paradigms for understanding strong correlation effects and unconventional superconductivity (SC). Recent large-scale density matrix renormalization group simulations on the extended t-J model have identified d-wave SC on the electron-doped side (with the next-nearest-neighbor hopping t 2 > 0) but a dominant charge density wave (CDW) order on the hole-doped side (t 2 < 0), which is inconsistent with the SC of hole-doped cuprate compounds. We re-examine the ground-state phase diagram of the extended t-J model by employing the state-of-the-art density matrix renormalization group calculations with much enhanced bond dimensions, allowing more accurate determination of the ground state. On six-leg cylinders, while different CDW phases are identified on the hole-doped side for the doping range δ = 1/16 – 1/8, a SC phase emerges at a lower doping regime, with algebraically decaying pairing correlations and d-wave symmetry. On the wider eight-leg systems, the d-wave SC also emerges on the hole-doped side at the optimal 1=8 doping, demonstrating the winning of SC over CDW by increasing the system width. Furthermore, our results not only suggest a new path to SC in general t-J model through weakening the competing charge orders, but also provide a unified understanding on the SC of both hole- and electron-doped cuprate superconductors.
Benchmarks and results of the two-band Hubbard model from the Gutzwiller conjugate gradient minimization theory
Ground-state properties, such as energies and double occupancies, of a one-dimensional two-band Hubbard model are calculated using a first-principles Gutzwiller conjugate gradient minimization theory. The favorable agreement with the results from the density matrix renormalization group theory demonstrates the accuracy of our method. A rotationally invariant approach is further incorporated into the method to greatly reduce the computational complexity with a speedup of approximately 50 times. Moreover, we investigate the Mott transition between a metal and a Mott insulator by evaluating the charge gap. In conclusion, with greatly reduced computational effort, our method reproduces the phase diagram in reasonable agreement with the density matrix renormalization group theory.
Block2 : A comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond
block2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms. In addition, it carries special optimizations for ab initio electronic structure Hamiltonians and implements many quantum chemistry extensions to the density matrix renormalization group, such as dynamical correlation theories. The code is designed with an emphasis on flexibility, extensibility, and efficiency and to support integration with external numerical packages. Here, we explain the design principles and currently supported features and present numerical examples in a range of applications.
Nonequilibrium spintronic transport through Kondo impurities
In this work we analyze the nonequilibrium transport through a quantum impurity (quantum dot or molecule) attached to ferromagnetic leads by using a hybrid numerical renormalization group–time-dependent density matrix renormalization group thermofield quench approach. For this, we study the bias dependence of the differential conductance through the system, which shows a finite zero-bias peak, characteristic of the Kondo resonance and reminiscent of the equilibrium local density of states. In the nonequilibrium settings, the resonance in the differential conductance is also found to decrease with increasing the lead spin polarization. The latter induces an effective exchange field that lifts the spin degeneracy of the dot level. Therefore, as we demonstrate, the Kondo resonance can be restored by counteracting the exchange field with a finite external magnetic field applied to the system. Lastly, we investigate the influence of temperature on the nonequilibrium conductance, focusing on the split Kondo resonance. Our work thus provides an accurate quantitative description of the spin-resolved transport properties relevant for quantum dots and molecules embedded in magnetic tunnel junctions.
Magnetic properties of alternating Hubbard ladders
We explore the Hubbard Hamiltonian on ladders where the number of sites per rung alternates between two and three. These geometries are bipartite with nonequal or equal number of sites on the two sublattices. Thus they share a key feature of the Hubbard model in a class of lattices which Lieb has shown analytically to exhibit long-range ferrimagnetic order while being amenable to powerful numeric approaches developed for quasi-one-dimensional geometries. The density matrix renormalization group (DMRG) method is used to obtain the groundstate properties, e.g., excitation gaps, charge and spin densities as well as their correlation functions at half filling. We show the existence of long-range ferrimagnetic order in the one-dimensional ladder geometries. Our work provides detailed quantitative results which complement the general theorem of Lieb for generalized bipartite lattices. It also addresses the issue of how the alternation between quasi-long-range order and spin liquid behavior for uniform ladders with odd and even numbers of legs might be affected by a regular alternation pattern.
Superconducting valence bond fluid in lightly doped eight-leg $t-J$ cylinders
Superconductivity in doped quantum paramagnets has been a subject of long theoretical inquiry. In this work, we report a density matrix renormalization group study of lightly doped $t-J$ models on the finite-width square lattice (doped hole densities $δ$ = 1/12 and 1/8) with parameters for which previous studies have suggested that the undoped system in 2D is either a quantum spin liquid or a valence bond crystal. Our studies are performed on cylinders with width up to 8. Here, ground-state correlations are found to be nearly identical for the “doped quantum spin liquid” and “doped valence bond crystal.” Upon increasing the cylinder widths from 4 to 8, we observed a significant strengthening of the quasi-long-range superconducting correlations and a dramatic suppression of any “competing” charge density wave order. Extrapolating from the observed behavior of the width eight cylinders, we speculate that the system has a nodeless $d$-wave superconducting ground state in the 2D limit.
Magnetic states of the quasi-one-dimensional iron chalcogenide Ba 2 FeS 3
Quasi-one-dimensional iron-based ladders and chains, with the 3d iron electronic density n=6, are attracting considerable attention. Recently, a new iron chain system Ba 2 FeS 3 , also with n=6, was prepared under high-pressure and high-temperature conditions. Here the magnetic and electronic phase diagrams are theoretically studied for this quasi-one-dimensional compound. Based on first-principles calculations, a strongly anisotropic one-dimensional electronic band behavior near the Fermi level was observed. In addition, a three-orbital electronic Hubbard model for this chain was constructed. Introducing the Hubbard and Hund couplings and studying the model via the density matrix renormalization group (DMRG) method, we studied the ground-state phase diagram. A robust staggered ↑-↓-↑-↓ AFM region was unveiled in the chain direction, consistent with our density functional theory (DFT) calculations. Furthermore, at intermediate Hubbard U coupling strengths, this system was found to display an orbital selective Mott phase (OSMP) with one localized orbital and two itinerant metallic orbitals. At very large U/W (W=bandwidth), the system displays Mott insulator characteristics, with two orbitals half-filled and one doubly occupied. Our results for high pressure Ba 2 FeS 3 provide guidance to experimentalists and theorists working on this one-dimensional iron chalcogenide chain material.
Majorana zero modes in Y -shape interacting Kitaev wires
Motivated by the recent experimental realization of minimal Kitaev chains using quantum dots, we investigate the Majorana zero modes (MZM) in Y-shape Kitaev wires. We solve the associated Kitaev models analytically at the sweet spot (t h = Δ) and derive the exact form of MZM wave-functions in this geometry. We observed exotic multi-site MZMs located near the junction center, on the nearby edge sites of each leg. This result is important for potential braiding of Majoranas and the performance of Y-junctions made from arrays of quantum dots. Furthermore, we study the stability of local (single-site) and multi-site MZMs modes in the presence of Coulomb repulsion, using density matrix renormalization group theory. Our local density-of-states calculation shows that these multi-site MZMs are as equally topologically protected as the single-site MZMs when in the presence of Coulomb repulsion or when away from the sweet-spot.
Algebraic Hastatic Order in One-Dimensional Two-Channel Kondo Lattice
The two-channel Kondo lattice likely hosts a rich array of phases, including hastatic order, a channel symmetry breaking heavy Fermi liquid. In this work, we revisit its one-dimensional phase diagram using density matrix renormalization group and, in contrast to previous work, find algebraic hastatic orders generically for stronger couplings. These are heavy Tomonaga-Luttinger liquids with nonanalyticities at Fermi vectors captured by hastatic density waves. We also find a predicted additional nonlocal order parameter due to interference between hastatic spinors, not present at large N, and residual repulsive interactions at strong coupling suggesting non-Fermi-liquid physics in higher dimensions.
π phase shift across stripes in a charge density wave system
Many strongly correlated materials are characterized by deeply intertwined charge and spin order. Besides their high superconducting transition temperatures, one of the central features of these complex patterns in cuprates is a phase shift which occurs across lines of decreased hole density. That is, when doped away from their antiferromagnetic phase, the additional charge is not distributed uniformly, but rather in “stripes.” The sublattices preferentially occupied by up and down spin are reversed across these stripes, a phenomenon referred to as a “π phase shift.” Many of the spin-charge patterns, including the π phase shift, are reproduced by density matrix renormalization group and quantum Monte Carlo calculations of simplified tight binding (repulsive Hubbard) models. In this paper we demonstrate that this sublattice reversal is generic by considering the corresponding phenomenon in the attractive Hubbard Hamiltonian, where a charge density wave phase forms at half filling. Here, we introduce charge stripes via an appropriate local chemical potential; measurements of charge correlation across the resulting lines of lowered density reveal a clear π phase.