361 research outputs found
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 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
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