Computational Quantum Many-Body Physics

Using computational many-body techniques our group studies the rich physics of strongly interacting quantum matter both in thermodynamic equilibrium, especially at low temperatures, as well as far from equilibrium.

 

Our research includes the dynamics of out of equilibrium quantum many-body systems and their thermalization process, as well as situations where statistical mechanics fails and new dynamical phases of matter emerge, for example due to strong disorder in the case of many-body localization. We are further interested in the physics of periodically driven many-body systems and also study open many-body systems undergoing nonunitary dynamics. A particularly interesting and universal aspect in generic many-body systems is the dynamics of quantum information, which can be quantified either by entanglement measures or out-of-time-order correlators, revealing how quantum information spreads through the system, which is related to thermalization and quantum chaos.

Quantum many-body systems are generically difficult to study due to the exponential number of degrees of freedom in terms of the number of particles, requiring high performance algorithms to access the universal physics. We use massively parallel exact diagonalization and exact time evolution techniques as well as tensor network methods and quantum Monte Carlo algorithms to tackle this challenging problem.

A selection of recent research highlights is listed below.

 

 

Many-body localization edge in the random-field Heisenberg chain

David J. Luitz, Nicolas Laflorencie, and Fabien Alet

We present a large-scale exact diagonalization study of the one-dimensional spin-1/2 Heisenberg model in a random magnetic field. In order to access properties at varying energy densities across the entire spectrum for system sizes up to L=22 spins, we use a spectral transformation which can be applied in a massively parallel fashion. Our results allow for an energy-resolved interpretation of the many-body localization transition including the existence of an extensive many-body mobility edge. The ergodic phase is well characterized by Gaussian orthogonal ensemble statistics, volume-law entanglement, and a full delocalization in the Hilbert space. Conversely, the localized regime displays Poisson statistics, area-law entanglement, and nonergodicity in the Hilbert space where a true localization never occurs. We perform finite-size scaling to extract the critical edge and exponent of the localization length divergence.

 

Phys. Rev. B 91, 081103(R) (2015)

Information propagation in isolated quantum systems

David J. Luitz and Yevgeny Bar Lev

Entanglement growth and out-of-time-order correlators (OTOC) are used to assess the propagation of information in isolated quantum systems. In this work, using large scale exact time evolution we show that for weakly disordered nonintegrable systems information propagates behind a ballistically moving front, and the entanglement entropy growths linearly in time. For stronger disorder the motion of the information front is algebraic and subballistic and is characterized by an exponent, which depends on the strength of the disorder, similarly to the sublinear growth of the entanglement entropy. We show that the dynamical exponent associated with the information front coincides with the exponent of the growth of the entanglement entropy for both weak and strong disorder. We also demonstrate that the temporal dependence of the OTOC is characterized by a fast nonexponential growth, followed by a slow saturation after the passage of the information front. Finally, we discuss the implications of this behavioral change on the growth of the entanglement entropy.

 

Phys. Rev. B 96, 020406(R) (2017)

Periodic and quasiperiodic revivals in periodically driven interacting quantum systems

David J. Luitz, Achilleas Lazarides, and Yevgeny Bar Lev

Recently it has been shown that interparticle interactions generically destroy dynamical localization in periodically driven systems, resulting in diffusive transport and heating. In this Rapid Communication we rigorously construct a family of interacting driven systems which are dynamically localized and effectively decoupled from the external driving potential. We show that these systems exhibit tunable periodic or quasiperiodic revivals of the many-body wave function and thus of all physical observables. By numerically examining spinless fermions on a one-dimensional lattice we show that the analytically obtained revivals of such systems remain stable for finite systems with open boundary conditions while having a finite lifetime in the presence of static spatial disorder. We find this lifetime to be inversely proportional to the disorder strength.

Phys. Rev. B 97, 020303(R) (2018)

Absence of dynamical localization in interacting driven systems

David J. Luitz, Yevgeny Bar Lev, Achilleas Lazarides

Using a numerically exact method we study the stability of dynamical localization to the addition of interactions in a periodically driven isolated quantum system which conserves only the total number of particles. We find that while even infinitesimally small interactions destroy dynamical localization, for weak interactions density transport is significantly suppressed and is asymptotically diffusive, with a diffusion coefficient proportional to the interaction strength. For systems tuned away from the dynamical localization point, even slightly, transport is dramatically enhanced and within the largest accessible systems sizes a diffusive regime is only pronounced for sufficiently small detunings.

 

SciPost Phys. 3, 029 (2017)

The ergodic side of the many-body localization transition

David J. Luitz and Yevgeny Bar Lev

Recent studies point towards nontriviality of the ergodic phase in systems exhibiting many-body localization (MBL), which shows subexponential relaxation of local observables, subdiffusive transport and sublinear spreading of the entanglement entropy. Here we review the dynamical properties of this phase and the available numerically exact and approximate methods for its study. We discuss in which sense this phase could be considered ergodic and present possible phenomenological explanations of its dynamical properties. We close by analyzing to which extent the proposed explanations were verified by numerical studies and present the open questions in this field.

Annalen der Physik 529, 1600350 (2017)

Anomalous Thermalization in Ergodic Systems

David J. Luitz and Yevgeny Bar Lev

It is commonly believed that quantum isolated systems satisfying the eigenstate thermalization hypothesis (ETH) are diffusive. We show that this assumption is too restrictive since there are systems that are asymptotically in a thermal state yet exhibit anomalous, subdiffusive thermalization. We show that such systems satisfy a modified version of the ETH ansatz and derive a general connection between the scaling of the variance of the off-diagonal matrix elements of local operators, written in the eigenbasis of the Hamiltonian, and the dynamical exponent. We find that for subdiffusively thermalizing systems the variance scales more slowly with system size than expected for diffusive systems. We corroborate our findings by numerically studying the distribution of the coefficients of the eigenfunctions and the off-diagonal matrix elements of local operators of the random field Heisenberg chain, which has anomalous transport in its thermal phase. Surprisingly, this system also has non-Gaussian distributions of the eigenfunctions, thus, directly violating Berry’s conjecture.

Phys. Rev. Lett. 117, 170404 (2016)