AI Article Synopsis
- Many-body localized Hamiltonians display area law entanglement, allowing efficient representation of low entanglement states using matrix product states (MPS), which is critical for algorithms like density matrix renormalization group (DMRG).
- Two new algorithms, shift-and-invert MPS (SIMPS) and excited state DMRG, are proposed for finding highly excited eigenstates of many-body localized systems, using unique techniques like modified sweeping and Hamiltonian inversion.
- The effectiveness of these methods is confirmed by analyzing the eigenstate thermalization hypothesis breakdown, observing entanglement saturation, and creating local excitations in the random field Heisenberg model.
Article Abstract
A key property of many-body localized Hamiltonians is the area law entanglement of even highly excited eigenstates. Matrix product states (MPS) can be used to efficiently represent low entanglement (area law) wave functions in one dimension. An important application of MPS is the widely used density matrix renormalization group (DMRG) algorithm for finding ground states of one-dimensional Hamiltonians. Here, we develop two algorithms, the shift-and-invert MPS (SIMPS) and excited state DMRG which find highly excited eigenstates of many-body localized Hamiltonians. Excited state DMRG uses a modified sweeping procedure to identify eigenstates, whereas SIMPS applies the inverse of the shifted Hamiltonian to a MPS multiple times to project out the targeted eigenstate. To demonstrate the power of these methods, we verify the breakdown of the eigenstate thermalization hypothesis in the many-body localized phase of the random field Heisenberg model, show the saturation of entanglement in the many-body localized phase, and generate local excitations.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevLett.118.017201 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Entropy-based methods for formulating bottom-up ultra-coarse-grained models.
J Chem Phys
January 2025
Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA.
Bottom-up coarse-grained (CG) modeling is an effective means of bypassing the limited spatiotemporal scales of conventional atomistic molecular dynamics while retaining essential information from the atomistic model. A central challenge in CG modeling is the trade-off between accuracy and efficiency, as the inclusion of often pivotal many-body interaction terms in the CG force-field renders simulation markedly slower than simple pairwise models. The Ultra Coarse-Graining (UCG) method incorporates many-body terms through discrete internal state variables that modulate the CG force-field according to, e.
View Article and Find Full Text PDFCompletely Multipolar Model for Many-Body Water-Ion and Ion-Ion Interactions.
J Phys Chem Lett
January 2025
Kenneth S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, California 94720, United States.
This work constructs an advanced force field, the Completely Multipolar Model (CMM), to quantitatively reproduce each term of an energy decomposition analysis (EDA) for aqueous solvated alkali metal cations and halide anions and their ion pairings. We find that all individual EDA terms remain well-approximated in the CMM for ion-water and ion-ion interactions, except for polarization, which shows errors due to the partial covalency of ion interactions near their equilibrium. We quantify the onset of the dative bonding regime by examining the change in molecular polarizability and Mayer bond indices as a function of distance, showing that partial covalency manifests by breaking the symmetry of atomic polarizabilities while strongly damping them at short-range.
View Article and Find Full Text PDFReviving the Lieb-Schultz-Mattis theorem in open quantum systems.
Natl Sci Rev
January 2025
Institute for Advanced Study, Tsinghua University, Beijing 100084, China.
In closed systems, the celebrated Lieb-Schultz-Mattis (LSM) theorem states that a one-dimensional locally interacting half-integer spin chain with translation and spin rotation symmetries cannot have a non-degenerate gapped ground state. However, the applicability of this theorem is diminished when the system interacts with a bath and loses its energy conservation. In this letter, we propose that the LSM theorem can be revived in the entanglement Hamiltonian when the coupling to the bath renders the system short-range correlated.
View Article and Find Full Text PDFStructural Origin of Dynamic Heterogeneity in Supercooled Liquids.
J Phys Chem B
January 2025
Research Center for Advanced Science and Technology, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan.
As a liquid is supercooled toward the glass transition point, its dynamics slow significantly, provided that crystallization is avoided. With increased supercooling, the particle dynamics become more spatially heterogeneous, a phenomenon known as dynamic heterogeneity. Since its discovery, this characteristic of metastable supercooled liquids has garnered considerable attention in glass science.
View Article and Find Full Text PDFQuantum Thermodynamics of Nonequilibrium Processes in Lattice Gauge Theories.
Phys Rev Lett
December 2024
Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA.
A key objective in nuclear and high-energy physics is to describe nonequilibrium dynamics of matter, e.g., in the early Universe and in particle colliders, starting from the standard model of particle physics.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!