38 research outputs found
Crystalline topological phases as defect networks
A crystalline topological phase is a topological phase with spatial
symmetries. In this work, we give a very general physical picture of such
phases: a topological phase with spatial symmetry (with internal symmetry
) is described by a *defect network*: a -symmetric
network of defects in a topological phase with internal symmetry
. The defect network picture works both for
symmetry-protected topological (SPT) and symmetry-enriched topological (SET)
phases, in systems of either bosons or fermions. We derive this picture both by
physical arguments, and by a mathematical derivation from the general framework
of [Thorngren and Else, Phys. Rev. X 8, 011040 (2018)]. In the case of
crystalline SPT phases, the defect network picture reduces to a previously
studied dimensional reduction picture, thus establishing the equivalence of
this picture with the general framework of Thorngren and Else applied to
crystalline SPTs.Comment: 13 pages + 2 pages of appendices. v3 published version, with better
justification of the equivalence relatio
Collisionless dynamics of general non-Fermi liquids from hydrodynamics of emergent conserved quantities
Given the considerable theoretical challenges in understanding strongly
coupled metals and non-Fermi liquids, it is valuable to have a framework to
understand properties of metals that are universal, in the sense that they must
hold in any metal. It has previously been argued that an infinite-dimensional
emergent symmetry group is such a property, at least for clean, compressible
metals. In this paper, we will show that such an emergent symmetry group has
very strong implications for the dynamics of the metal. Specifically, we show
that consideration of the hydrodynamics of the associated infinitely many
emergent conserved quantities automatically recovers the collisionless
Boltzmann equation that governs the dynamics of a Fermi liquid. Therefore, the
hydrodynamic prediction is that in the low-temperature, collisionless regime
where the emergent conservation laws hold, the dynamics and response to
external fields of a general spinless metal will be identical to a Fermi
liquid. We discuss some potential limitations to this general statement,
including the possibility of non-hydrodynamic modes. We also report some
interesting differences in the case of spinful metals.Comment: 10 pages + 3 pages appendices. v2 Some minor improvements and
clarification
Pre-thermal phases of matter protected by time-translation symmetry
In a periodically driven (Floquet) system, there is the possibility for new
phases of matter, not present in stationary systems, protected by discrete
time-translation symmetry. This includes topological phases protected in part
by time-translation symmetry, as well as phases distinguished by the
spontaneous breaking of this symmetry, dubbed "Floquet time crystals". We show
that such phases of matter can exist in the pre-thermal regime of
periodically-driven systems, which exists generically for sufficiently large
drive frequency, thereby eliminating the need for integrability or strong
quenched disorder that limited previous constructions. We prove a theorem that
states that such a pre-thermal regime persists until times that are nearly
exponentially-long in the ratio of certain couplings to the drive frequency. By
similar techniques, we can also construct stationary systems which
spontaneously break *continuous* time-translation symmetry. We argue
furthermore that for driven systems coupled to a cold bath, the pre-thermal
regime could potentially persist to infinite time.Comment: Published version, with new title and introductio
Fragile topological phases in interacting systems
Topological phases of matter are defined by their nontrivial patterns of
ground-state quantum entanglement, which is irremovable so long as the
excitation gap and the protecting symmetries, if any, are maintained. Recent
studies on noninteracting electrons in crystals have unveiled a peculiar
variety of topological phases, which harbors nontrivial entanglement that can
be dissolved simply by the the addition of entanglement-free, but charged,
degrees of freedom. Such topological phases have a weaker sense of robustness
than their conventional counterparts, and are therefore dubbed "fragile
topological phases." In this work, we show that fragile topology is a general
concept prevailing beyond systems of noninteracting electrons. Fragile
topological phases can generally occur when a system has a
charge conservation symmetry, such that only particles with one sign of the
charge are physically allowed (e.g. electrons but not positrons). We
demonstrate that fragile topological phases exist in interacting systems of
both fermions and of bosons.Comment: 14 pages. Comments welcome; v2: several discussions are improve
Prethermal Strong Zero Modes and Topological Qubits
We prove that quantum information encoded in some topological excitations,
including certain Majorana zero modes, is protected in closed systems for a
time scale exponentially long in system parameters. This protection holds even
at infinite temperature. At lower temperatures the decay time becomes even
longer, with a temperature dependence controlled by an effective gap that is
parametrically larger than the actual energy gap of the system. This
non-equilibrium dynamical phenomenon is a form of prethermalization, and occurs
because of obstructions to the equilibriation of edge or defect degrees of
freedom with the bulk. We analyze the ramifications for ordered and topological
phases in one, two, and three dimensions, with examples including Majorana and
parafermionic zero modes in interacting spin chains. Our results are based on a
non-perturbative analysis valid in any dimension, and they are illustrated by
numerical simulations in one dimension. We discuss the implications for
experiments on quantum-dot chains tuned into a regime supporting end Majorana
zero modes, and on trapped ion chains.Comment: 20 pages. v2: reorganized and added overview sectio