Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1608.06411 · Annalen der Physik

Density‐matrix renormalization group study of many‐body localization in floquet eigenstates

Carolyn Zhang, Frank Pollmann, S. L. Sondhi, Roderich Moessner

Published Mar 31, 2017• 13 citations
arXivHTMLPDF

Abstract

We generalize the recently introduced Density‐Matrix Renormalization Group (DMRG‐X) [Khemani et al, PRL 2016] algorithm to obtain Floquet eigenstates of one‐dimensional, periodically driven many‐body localized systems. This generalization is made possible by the fact that the time‐evolution operator for a period can be efficiently represented using a matrix‐product operator. We first benchmark the method by comparing to exact diagonalization for small systems. We then obtain Floquet eigenstates for larger systems and show unambiguously that the characteristic area‐law scaling remains robust. image

DOI
10.1002/andp.201600294

Related papers

Density-matrix renormalization group study of many-body localization in floquet eigenstates

Zhang, C., Pollmann, F., Shivaji L. Sondhi +1 more

We generalize the recently introduced Density-Matrix Renormalization Group (DMRG-X) [Khemani et al, PRL 2016] algorithm to obtain Floquet eigenstates of one-dimensional, periodically driven many-body localized systems. This generalization is made possible by the fact that the time-evolution operator for a period can be efficiently represented using a matrix-product operator. We first benchmark the method by comparing to exact diagonalization for small systems. We then obtain Floquet eigenstates for larger systems and show unambiguously that the characteristic area-law scaling remains robust.

•Jul 5, 2017•14 citations

Obtaining Highly Excited Eigenstates of Many-Body Localized Hamiltonians by the Density Matrix Renormalization Group Approach

Vedika Khemani, Frank Pollmann, Shivaji L. Sondhi

The eigenstates of many-body localized (MBL) Hamiltonians exhibit low entanglement. We adapt the highly successful density-matrix renormalization group method, which is usually used to find modestly entangled ground states of local Hamiltonians, to find individual highly excited eigenstates of MBL Hamiltonians. The adaptation builds on the distinctive spatial structure of such eigenstates. We benchmark our method against the well-studied random field Heisenberg model in one dimension. At moderate to large disorder, the method successfully obtains excited eigenstates with high accuracy, thereby enabling a study of MBL systems at much larger system sizes than those accessible to exact-diagonalization methods.

arXiv:1509.00483•Physical Review Letters•Jun 17, 2016•163 citations

Many-Body Localization in Periodically Driven Systems

Pedro Ponte, Zlatko Papić, François Huveneers +1 more

We consider disordered many-body systems with periodic time-dependent Hamiltonians in one spatial dimension. By studying the properties of the Floquet eigenstates, we identify two distinct phases: (i) a many-body localized (MBL) phase, in which almost all eigenstates have area-law entanglement entropy, and the eigenstate thermalization hypothesis (ETH) is violated, and (ii) a delocalized phase, in which eigenstates have volume-law entanglement and obey the ETH. The MBL phase exhibits logarithmic in time growth of entanglement entropy when the system is initially prepared in a product state, which distinguishes it from the delocalized phase. We propose an effective model of the MBL phase in terms of an extensive number of emergent local integrals of motion, which naturally explains the spectral and dynamical properties of this phase. Numerical data, obtained by exact diagonalization and time-evolving block decimation methods, suggest a direct transition between the two phases.

arXiv:1410.8518•Physical Review Letters•Apr 7, 2015•524 citations

Time evolution of one-dimensional Quantum Many Body Systems

Salvatore R. Manmana

The level of current understanding of the physics of time‐dependent strongly correlated quantum systems is far from complete, principally due to the lack of effective controlled approaches. Recently, there has been progress in the development of approaches for one‐dimensional systems. We describe recent developments in the construction of numerical schemes for general (one‐dimensional) Hamiltonians: in particular, schemes based on exact diagonalization techniques and on the density matrix renormalization group method (DMRG). We present preliminary results for spinless fermions with nearest‐neighbor‐interaction and investigate their accuracy by comparing with exact results.

arXiv:cond-mat/0502396•AIP conference proceedings•Jan 1, 2005•84 citations

Many-body localization and transition by density matrix renormalization group and exact diagonalization studies

S. P. Lim, D. N. Sheng

This paper focuses on developing a new algorithm (En-DMRG) for obtaining highly excited states of disordered and strongly interacting spin systems. This line of research is stimulated by the growing interest in understanding the many-body localized (MBL) state, which emerges in disordered interacting systems at high energy densities through a disorder-driven dynamic phase transition. By studying the one-dimensional Heisenberg spin chain (with up to 72 spins) in a random field, the authors demonstrate the accuracy of the method in obtaining energy eigenstates and the corresponding statistical results of the quantum system in the MBL phase. The method presented in this work has the potential to be applicable in a variety of quantum statistical physics problems, possibly including the MBL phase in higher dimensions.

arXiv:1510.08145•Physical review. B./Physical review. B•Jul 13, 2016•94 citations

Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems

R. M. Noack

In these lecture notes, we present a pedagogical review of a number of related numerically exact approaches to quantum many‐body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix and on methods extending exact diagonalization using renormalization group ideas, i.e., Wilson’s Numerical Renormalization Group (NRG) and White’s Density Matrix Renormalization Group (DMRG). These methods are standard tools for the investigation of a variety of interacting quantum systems, especially low‐dimensional quantum lattice models. We also survey extensions to the methods to calculate properties such as dynamical quantities and behavior at finite temperature, and discuss generalizations of the DMRG method to a wider variety of systems, such as classical models and quantum chemical problems. Finally, we briefly review some recent developments for obtaining a more general formulation of the DMRG in the context of matrix product states as well as recent progress in calculating the time evolution of quantum systems using the DMRG and the relationship of the foundations of the method with quantum information theory.

arXiv:cond-mat/0510321•AIP conference proceedings•Jan 1, 2005•118 citations
We generalize the recently introduced Density‐Matrix Renormalization Group (DMRG‐X) [Khemani et al, PRL 2016] algorithm to obtain Floquet eigenstates of one‐dimensional, periodically driven many‐body localized systems. This generalization is made possible by the fact that the time‐evolution operator for a period can be efficiently represented using a matrix‐product operator. We first benchmark the method by comparing to exact diagonalization for small systems. We then obtain Floquet eigenstates for larger systems and show unambiguously that the characteristic area‐law scaling remains robust. image
We generalize the recently introduced Density-Matrix Renormalization Group (DMRG-X) [Khemani et al, PRL 2016] algorithm to obtain Floquet eigenstates of one-dimensional, periodically driven many-body localized systems. This generalization is made possible by the fact that the time-evolution operator for a period can be efficiently represented using a matrix-product operator. We first benchmark the method by comparing to exact diagonalization for small systems. We then obtain Floquet eigenstates for larger systems and show unambiguously that the characteristic area-law scaling remains robust.
The eigenstates of many-body localized (MBL) Hamiltonians exhibit low entanglement. We adapt the highly successful density-matrix renormalization group method, which is usually used to find modestly entangled ground states of local Hamiltonians, to find individual highly excited eigenstates of MBL Hamiltonians. The adaptation builds on the distinctive spatial structure of such eigenstates. We benchmark our method against the well-studied random field Heisenberg model in one dimension. At moderate to large disorder, the method successfully obtains excited eigenstates with high accuracy, thereby enabling a study of MBL systems at much larger system sizes than those accessible to exact-diagonalization methods.
We consider disordered many-body systems with periodic time-dependent Hamiltonians in one spatial dimension. By studying the properties of the Floquet eigenstates, we identify two distinct phases: (i) a many-body localized (MBL) phase, in which almost all eigenstates have area-law entanglement entropy, and the eigenstate thermalization hypothesis (ETH) is violated, and (ii) a delocalized phase, in which eigenstates have volume-law entanglement and obey the ETH. The MBL phase exhibits logarithmic in time growth of entanglement entropy when the system is initially prepared in a product state, which distinguishes it from the delocalized phase. We propose an effective model of the MBL phase in terms of an extensive number of emergent local integrals of motion, which naturally explains the spectral and dynamical properties of this phase. Numerical data, obtained by exact diagonalization and time-evolving block decimation methods, suggest a direct transition between the two phases.
The level of current understanding of the physics of time‐dependent strongly correlated quantum systems is far from complete, principally due to the lack of effective controlled approaches. Recently, there has been progress in the development of approaches for one‐dimensional systems. We describe recent developments in the construction of numerical schemes for general (one‐dimensional) Hamiltonians: in particular, schemes based on exact diagonalization techniques and on the density matrix renormalization group method (DMRG). We present preliminary results for spinless fermions with nearest‐neighbor‐interaction and investigate their accuracy by comparing with exact results.
This paper focuses on developing a new algorithm (En-DMRG) for obtaining highly excited states of disordered and strongly interacting spin systems. This line of research is stimulated by the growing interest in understanding the many-body localized (MBL) state, which emerges in disordered interacting systems at high energy densities through a disorder-driven dynamic phase transition. By studying the one-dimensional Heisenberg spin chain (with up to 72 spins) in a random field, the authors demonstrate the accuracy of the method in obtaining energy eigenstates and the corresponding statistical results of the quantum system in the MBL phase. The method presented in this work has the potential to be applicable in a variety of quantum statistical physics problems, possibly including the MBL phase in higher dimensions.
In these lecture notes, we present a pedagogical review of a number of related numerically exact approaches to quantum many‐body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix and on methods extending exact diagonalization using renormalization group ideas, i.e., Wilson’s Numerical Renormalization Group (NRG) and White’s Density Matrix Renormalization Group (DMRG). These methods are standard tools for the investigation of a variety of interacting quantum systems, especially low‐dimensional quantum lattice models. We also survey extensions to the methods to calculate properties such as dynamical quantities and behavior at finite temperature, and discuss generalizations of the DMRG method to a wider variety of systems, such as classical models and quantum chemical problems. Finally, we briefly review some recent developments for obtaining a more general formulation of the DMRG in the context of matrix product states as well as recent progress in calculating the time evolution of quantum systems using the DMRG and the relationship of the foundations of the method with quantum information theory.