Obtaining highly-excited eigenstates of many-body localized Hamiltonians by the density matrix renormalization group

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 many body localized 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, we find that 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.Comment: Published version. Slightly expanded discussion; supplement adde

A Bionic Coulomb Phase on the Pyrochlore Lattice

A class of three dimensional classical lattice systems with macroscopic ground state degeneracies, most famously the spin ice system, are known to exhibit "Coulomb" phases wherein long wavelength correlations within the ground state manifold are described by an emergent Maxwell electrodynamics. We discuss a new example of this phenomenon-the four state Potts model on the pyrochlore lattice-where the long wavelength description now involves three independent gauge fields as we confirm via simulation. The excitations above the ground state manifold are bions, defects that are simultaneously charged under two of the three gauge fields, and exhibit an entropic interaction dictated by these charges. We also show that the distribution of flux loops shows a scaling with loop length and system size previously identified as characteristic of Coulomb phases

Defining Time Crystals via Representation Theory

Time crystals are proposed states of matter which spontaneously break time translation symmetry. There is no settled definition of such states. We offer a new definition which follows the traditional recipe for Wigner symmetries and order parameters. Supplementing our definition with a few plausible assumptions we find that a) systems with time independent Hamiltonians should not exhibit TTSB while b) the recently studied $\pi$ spin glass/Floquet time crystal can be viewed as breaking a global internal symmetry and as breaking time translation symmetry as befits its two names

Absolute Stability and Spatiotemporal Long-Range Order in Floquet systems

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 sub-manifolds 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.Comment: Published version. Minor typos corrected, some discussions expande

On the phase structure of driven quantum systems

Clean and interacting periodically driven quantum 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 non-trivial periodic dynamics. We illustrate these ideas in driven spin chains with Ising symmetry.Comment: v3 - published version. Discussions expanded/clarified in few place

Mott, Floquet, and the response of periodically driven Anderson insulators

We consider periodically driven Anderson insulators. The short time behavior for weak, monochromatic, uniform electric fields is given by linear response theory and was famously derived by Mott. We go beyond this to consider both long times---which is the physics of Floquet late time states---and strong electric fields. This results in a `phase diagram' in the frequency-field strength plane, in which we identify four distinct regimes. These are: a linear response regime dominated by pre-existing Mott resonances, which exists provided Floquet saturation is not reached within a period; a non-linear perturbative regime, which exhibits multiphoton-absorption in response to the field; a near-adiabatic regime, which exhibits a primarily reactive response spread over the entire sample and is insensitive to pre-existing resonances; and finally an enhanced dissipative regime.Comment: 15 pages, 9 figure