Showing papers by "Shivaji Lal Sondhi published in 2016"

Phase Structure of Driven Quantum Systems.

Abstract: Clean and interacting periodically driven systems are believed to exhibit a single, trivial "infinite-temperature" Floquet-ergodic phase. In contrast, here we show that their disordered Floquet many-body localized counterparts can exhibit distinct ordered phases delineated by sharp transitions. Some of these are analogs of equilibrium states with broken symmetries and topological order, while others-genuinely new to the Floquet problem-are characterized by order and nontrivial periodic dynamics. We illustrate these ideas in driven spin chains with Ising symmetry.

Absolute stability and spatiotemporal long-range order in Floquet systems

Abstract: Recent work has shown that a variety of novel phases of matter arise in periodically driven Floquet systems. Among these are many-body localized phases which spontaneously break global symmetries and exhibit novel multiplets of Floquet eigenstates separated by quantized quasienergies. Here we show that these properties are stable to all weak local deformations of the underlying Floquet drives---including those that explicitly break the defining symmetries---and that the models considered until now occupy submanifolds within these larger ``absolutely stable'' phases. While these absolutely stable phases have no explicit global symmetries, they spontaneously break Hamiltonian-dependent emergent symmetries, and thus continue to exhibit the novel multiplet structure. The multiplet structure in turn encodes characteristic oscillations of the emergent order parameter at multiples of the fundamental period. Altogether these phases exhibit a form of simultaneous long-range order in space and time which is new to quantum systems. We describe how this spatiotemporal order can be detected in experiments involving quenches from a broad class of initial states.

Phase structure of one-dimensional interacting Floquet systems. I. Abelian symmetry-protected topological phases

Abstract: Phases of matter are traditionally seen as families of static systems exhibiting the same long-distance and low-energy correlations. In this work, the authors propose and classify a new family of phases of matter. They are novel insofar as they are intrinsically driven and out of equilibrium --- they can only be realized in systems with time-dependent Hamiltonians. The phases we consider arise in 1D periodically driven systems, in the presence of strong disorder and interactions, and are similar to but qualitatively distinct from the symmetry-protected topological phases now well known in the equilibrium setting. In a companion paper, the authors examine similar intrinsically driven families of states with long-range order, and an order parameter that oscillates at a frequency that is robustly an integer multiple of the underlying drive frequency.

Phase structure of one-dimensional interacting Floquet systems. II. Symmetry-broken phases

Abstract: Recent work suggests that a sharp definition of ``phase of matter'' can be given for periodically driven ``Floquet'' quantum systems exhibiting many-body localization. In this work, we propose a classification of the phases of interacting Floquet localized systems with (completely) spontaneously broken symmetries; we focus on the one-dimensional case, but our results appear to generalize to higher dimensions. We find that the different Floquet phases correspond to elements of $Z(G)$, the center of the symmetry group in question. In a previous paper [C. W. von Keyserlingk and S. L. Sondhi, preceding paper, Phys. Rev. B 93, 245145 (2016)], we offered a companion classification of unbroken, i.e., paramagnetic phases.

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

Abstract: 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.

Efficient variational diagonalization of fully many-body localized Hamiltonians

Abstract: The phenomenon of many-body localization generalizes Anderson localization to interacting systems. Understanding this conceptually novel phenomenon requires a study of many-body eigenstates at finite energy densities. This is a very challenging task since the most efficient numerical methods such as, e.g., the density matrix renormalization group method, can only access the ground state and low lying excitations. In this work, the authors introduce a unitary tensor network based variational method that approximately finds all many-body eigenstates of fully localized Hamiltonians and scales polynomially with system size. The usefulness of their approach is demonstrated by considering the Heisenberg chain in a strongly disordered magnetic field.

Interaction-stabilized steady states in the driven O(N) model

Abstract: We study periodically driven bosonic scalar field theories in the infinite $N$ limit. It is well known that the free theory can undergo parametric resonance under monochromatic modulation of the mass term and thereby absorb energy indefinitely. Interactions in the infinite $N$ limit terminate this increase for any choice of the UV cutoff and driving frequency. The steady state has nontrivial correlations and is synchronized with the drive. The $O(N)$ model at infinite $N$ provides the first example of a clean interacting quantum system that does not heat to infinite temperature at any drive frequency.

Order by disorder and by doping in quantum Hall valley ferromagnets

Abstract: We examine the Si(111) multivalley quantum Hall system and show that it exhibits an exceptionally rich interplay of broken symmetries and quantum Hall ordering already near integer fillings $\ensuremath{ u}$ in the range $\ensuremath{ u}=0--6$. This six-valley system has a large ${[\text{SU}(2)]}^{3}\ensuremath{\rtimes}{D}_{3}$ symmetry in the limit where the magnetic length is much larger than the lattice constant. We find that the discrete ${D}_{3}$ factor breaks over a broad range of fillings at a finite-temperature transition to a discrete nematic phase. As $T\ensuremath{\rightarrow}0$, the ${[\text{SU}(2)]}^{3}$ continuous symmetry also breaks: completely near $\ensuremath{ u}=3$, to a residual ${[\text{U}(1)]}^{2}\ifmmode\times\else\texttimes\fi{}\text{SU}(2)$ near $\ensuremath{ u}=2$ and 4, and to a residual $\text{U}(1)\ifmmode\times\else\texttimes\fi{}{[\text{SU}(2)]}^{2}$ near $\ensuremath{ u}=1$ and 5. Interestingly, the symmetry breaking near $\ensuremath{ u}=2,\phantom{\rule{0.28em}{0ex}}4$ and $\ensuremath{ u}=3$ involves a combination of selection by thermal fluctuations known as ``order by disorder'' and a selection by the energetics of Skyrme lattices induced by moving away from the commensurate fillings, a mechanism we term ``order by doping.''

Emergent Symmetries and Absolutely Stable phases of Floquet systems

Abstract: Recent work has shown that a variety of driven phases of matter arise in Floquet systems. Among these are many-body localized phases which spontaneously break unitary symmetries and exhibit novel multiplets of Floquet eigenstates separated by quantized quasienergies. Here we show that these properties are stable to {\it all} weak local deformations of the underlying Floquet drives, and that the models considered until now occupy sub-manifolds within these larger "absolutely stable" phases. While these absolutely stable phases have no explicit Hamiltonian independent global symmetries, they spontaneously break Hamiltonian dependent {\it emergent} unitary or anti-unitary symmetries, and thus continue to exhibit the novel multiplet structure. We show that the out of equilibrium dynamics exhibit a lack of synchrony with the drive characterized by infinitely many distinct frequencies, most incommensurate with the fundamental period --- i.e., these phases look like time glasses. Floquet eigenstates, however, exhibit a purely commensurate temporal crystalline periodicity for a special class of bilocal operators with infinite separation which reflects the dynamics of the order parameter for the emergent symmetries.