Engineering Papers⌕ Search
Home/Archive/DOE OSTI

DOE OSTI · 2927986

Fermionic Isometric Tensor Network States in Two Dimensions

Dai, Zhehao [University of California, Berkeley, CA (United States); University of Pittsburgh, PA (United States)] (ORCID:0000000237895683)·Wu, Yantao [RIKEN iTHEMS, Saitama (Japan); University of California, Berkeley, CA (United States)] (ORCID:0000000323609647)·Wang, Taige [University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)] (ORCID:000000017227915X)·Zaletel, Michael P. [University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)]
View original source ↗Read source document ↗Export metadata ↓

Abstract

We generalize isometric tensor network states to fermionic systems, paving the way for efficient adaptations of 1D tensor network algorithms to 2D fermionic systems. As the first application of this formalism, we developed and benchmarked a time-evolving block-decimation (TEBD) algorithm for real-time and imaginary-time evolution. The imaginary-time evolution produces ground-state energies for gapped systems, systems with a Dirac point, and systems with gapless edge modes to good accuracy. Here, the real-time TEBD captures the scattering of two fermions and the chiral edge dynamics on the boundary of a Chern insulator.

Explore related subjects

2-dimensional systems75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITYLattice models in condensed matterTensor network methodslattice models in condensed mattertensor network methods

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Dai, Zhehao [University of California, Berkeley, CA (United States); University of Pittsburgh, PA (United States)] (ORCID:0000000237895683), Wu, Yantao [RIKEN iTHEMS, Saitama (Japan); University of California, Berkeley, CA (United States)] (ORCID:0000000323609647), Wang, Taige [University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)] (ORCID:000000017227915X), Zaletel, Michael P. [University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)]. 2025-01-14. Fermionic Isometric Tensor Network States in Two Dimensions. https://doi.org/10.1103/physrevlett.134.026502

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related reports

DOE OSTI2026

Space-Charge-Limited van der Waals Spin Transistor

Integrating semiconducting and magnetic materials could combine transistorlike operation with nonvolatility and enable architectures such as logic in memory. Here, in this work, we employ correlated electrical transport and scanning nitrogen-vacancy center magnetic imaging to elucidate a spin transistor concept that amalgamates vertical and lateral hopping transport inside a 2D antiferromagnetic semiconductor, mechanistically distinct from vertical tunneling devices. Our device, based on a monolayer-bilayer junction in CrSBr, displays giant, gate-tunable magnetoresistance driven by the dual action of electrostatic doping on space-charge-limited lateral conduction and interlayer exchange coupling. Moreover, we visualize a field-trainable, layer-sharing effect that selects between coherent or domain-wall reversal at the spin-flip transition, enabling multilevel, memristive conductance states. Our layer-dependent space charge mechanism for convergent electrical and magnetic control opens opportunities to address limitations in contemporary computing.

2-dimensional systems↗
DOE OSTI2026

One-dimensional neutron diffraction from layered graphite: Reciprocal space structure and grating behavior

In this work we report observations of one-dimensional neutron diffraction from highly oriented pyrolytic graphite (HOPG), where the scattering angle varies continuously with incident angle following classical grating-like behavior. The 2D polycrystalline structure of HOPG—with highly aligned layers along the 𝑐 axis but random in-plane rotations—creates planes of scattering intensity in reciprocal space at 𝑄 𝑐 =𝑛⁢(2⁢𝜋/𝑑) where 𝑑=3.35Å is the interlayer spacing. As the Ewald sphere sweeps through reciprocal space during sample rotation, it continuously intersects these planes, producing the observed angular dispersion. We observe both first-order (𝑛=1) and second-order (𝑛=2) diffraction at conventional scattering angles (25°–70°), with peak positions that remain temperature-independent between 10 K and 294 K and follow quantitative agreement with momentum conservation 𝑄 𝑐 =𝑘⁢[sin⁡𝜓−sin⁡𝜓 𝑓 ]=𝑛⁢(2⁢𝜋/𝑑). X-ray diffraction under similar conditions shows no comparable behavior, confirming that sharp nuclear-vacuum contrast is essential. While diffraction intensities are weak (∼10 −6 of Bragg peaks), the observations demonstrate how the interplay of atomic-scale periodicity, nuclear contrast, and structural disorder enables observation of continuous diffraction curves at thermal neutron wavelengths, illustrating how HOPG's unique microstructure determines its scattering properties beyond conventional Bragg diffraction.

2-dimensional systems↗
DOE OSTI2026

Diagonal isometric form for tensor network states in two dimensions

Isometric tensor network states (isoTNS) generalize the isometric form of the one-dimensional matrix product states to tensor networks in two and higher dimensions. Here, we introduce an alternative isometric form for isoTNS by incorporating auxiliary tensors to represent the orthogonality hypersurface. We implement the time evolving block decimation algorithm on this new isometric form and benchmark the method by computing ground states and the real time evolution of the transverse field Ising model in two dimensions on large square lattices of up to 1250 sites. Our results demonstrate that isoTNS can efficiently capture the entanglement structure of two-dimensional area law states. The short-time dynamics is also accurately reproduced even at the critical point. Our isoTNS formulation further allows for a natural extension to different lattice geometries, such as the honeycomb or kagome lattice.

2-dimensional systems↗