We present an introductory review of nonergodic dynamics in interacting many-body quantum systems, focusing on the phenomenon of many-body localization (MBL). We describe aspects of MBL and summarize the evidence for a crossover from the ergodic to the MBL regime in finite systems, using the paradigmatic XXZ model as an example. We then broaden the scope to other models to illustrate the generality of the phenomenon. We briefly touch on the largely unexplored relation between MBL and quantum computing.We present an introductory review of nonergodic dynamics in interacting many-body quantum systems, focusing on the phenomenon of many-body localization (MBL). We describe aspects of MBL and summarize the evidence for a crossover from the ergodic to the MBL regime in finite systems, using the paradigmatic XXZ model as an example. We then broaden the scope to other models to illustrate the generality of the phenomenon. We briefly touch on the largely unexplored relation between MBL and quantum computing.

quant-pharXiv:2604.12464Apr 15, 20260 citations

Studying many-body localization on a universal quantum computer

Sonika Johri, Daiwei Zhu, Nhung H. Nguyen +5 more

Bulletin of the American Physical SocietyMar 3, 20200 citations

Many-body localization as a large family of localized ground states

Maxime Dupont, Nicolas Laflorencie

Many-body localization (MBL) addresses the absence of thermalization in interacting quantum systems, with nonergodic high-energy eigenstates behaving as ground states, only area-law entangled. However, computing highly excited many-body eigenstates using exact methods is very challenging. Instead, we show that one can address high-energy MBL physics using ground-state methods, which are much more amenable to many efficient algorithms. We find that a localized many-body ground state of a given interacting disordered Hamiltonian ${\mathcal{H}}_{0}$ is a very good approximation for a high-energy eigenstate of a parent Hamiltonian, close to ${\mathcal{H}}_{0}$ but more disordered. This construction relies on computing the covariance matrix, easily achieved using density-matrix renormalization group for disordered Heisenberg chains up to $L=256$ sites.Many-body localization (MBL) addresses the absence of thermalization in interacting quantum systems, with nonergodic high-energy eigenstates behaving as ground states, only area-law entangled. However, computing highly excited many-body eigenstates using exact methods is very challenging. Instead, we show that one can address high-energy MBL physics using ground-state methods, which are much more amenable to many efficient algorithms. We find that a localized many-body ground state of a given interacting disordered Hamiltonian ${\mathcal{H}}_{0}$ is a very good approximation for a high-energy eigenstate of a parent Hamiltonian, close to ${\mathcal{H}}_{0}$ but more disordered. This construction relies on computing the covariance matrix, easily achieved using density-matrix renormalization group for disordered Heisenberg chains up to $L=256$ sites.

arXiv:1807.01313Physical review. B./Physical review. BJan 15, 201925 citations

Quantum Computation and Many Body Physics

Adam G. D’Souza

Jan 17, 20140 citations

A Many--Body Hamiltonian Approach to Quantum Computation

Mario Rasetti, Elena Tagliati, Paolo Zanardi A +1 more

Jan 1, 19960 citations

Real-time dynamics of one-dimensional and two-dimensional bosonic quantum matter deep in the many-body localized phase

Sunwoo Kim, Giuseppe De Tomasi, Markus Heyl

Recent experiments in quantum simulators have provided evidence for the many-body localized (MBL) phase in one-dimensional (1D) and two-dimensional (2D) bosonic quantum matter. The theoretical study of such a bosonic MBL phase, however, is a daunting task due to the unbounded nature of its Hilbert space. In this work, we introduce a method to compute the long-time real-time evolution of 1D and 2D bosonic systems in an MBL phase at strong disorder and weak interactions. We focus on local dynamical indicators that are able to distinguish an MBL phase from an Anderson localized one. In particular, we consider the temporal fluctuations of local observables, the spatiotemporal behavior of two-time correlators and out-of-time-correlators. We show that these few-body observables can be computed with a computational effort that depends only polynomially on the system size but is independent of the target time, by extending a recently proposed numerical method [G. De Tomasi, F. Pollmann, and M. Heyl, Phys. Rev. B 99, 241114(R) (2019)] to mixed states and bosons. Our method also allows us to surrogate our numerical study with analytical considerations of the time-dependent behavior of the studied quantities.Recent experiments in quantum simulators have provided evidence for the many-body localized (MBL) phase in one-dimensional (1D) and two-dimensional (2D) bosonic quantum matter. The theoretical study of such a bosonic MBL phase, however, is a daunting task due to the unbounded nature of its Hilbert space. In this work, we introduce a method to compute the long-time real-time evolution of 1D and 2D bosonic systems in an MBL phase at strong disorder and weak interactions. We focus on local dynamical indicators that are able to distinguish an MBL phase from an Anderson localized one. In particular, we consider the temporal fluctuations of local observables, the spatiotemporal behavior of two-time correlators and out-of-time-correlators. We show that these few-body observables can be computed with a computational effort that depends only polynomially on the system size but is independent of the target time, by extending a recently proposed numerical method [G. De Tomasi, F. Pollmann, and M. Heyl, Phys. Rev. B 99, 241114(R) (2019)] to mixed states and bosons. Our method also allows us to surrogate our numerical study with analytical considerations of the time-dependent behavior of the studied quantities.

arXiv:2105.12740Physical review. B./Physical review. BOct 25, 20214 citations

{\mathcal{H}}_{0}

is a very good approximation for a high-energy eigenstate of a parent Hamiltonian, close to

{\mathcal{H}}_{0}

but more disordered. This construction relies on computing the covariance matrix, easily achieved using density-matrix renormalization group for disordered Heisenberg chains up to

L=256

sites.