32 research outputs found
Quasilocal conservation laws from semicyclic irreducible representations of in spin- chains
We construct quasilocal conserved charges in the gapless ()
regime of the Heisenberg spin- chain, using semicyclic irreducible
representations of . These representations are
characterized by a periodic action of ladder operators, which act as generators
of the aforementioned algebra. Unlike previously constructed conserved charges,
the new ones do not preserve magnetization, i.e. they do not possess the
symmetry of the Hamiltonian. The possibility of application in relaxation
dynamics resulting from -breaking quantum quenches is discussed
Quasilocal conserved operators in isotropic Heisenberg spin 1/2 chain
Composing higher auxiliary-spin transfer matrices and their derivatives, we
construct a family of quasilocal conserved operators of isotropic Heisenberg
spin 1/2 chain and rigorously establish their linear independence from the
well-known set of local conserved charges.Comment: 5 + 6 pages in RevTex; v2: slightly revised version as accepted by
PR
Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
In a many-body quantum system, local operators in Heisenberg picture spread as time increases. Recent studies have attempted
to find features of that spreading which could distinguish between chaotic and
integrable dynamics. The operator entanglement - the entanglement entropy in
operator space - is a natural candidate to provide such a distinction. Indeed,
while it is believed that the operator entanglement grows linearly with time
in chaotic systems, numerics suggests that it grows only logarithmically in
integrable systems. That logarithmic growth has already been established for
non-interacting fermions, however progress on interacting integrable systems
has proved very difficult. Here, for the first time, a logarithmic upper bound
is established rigorously for all local operators in such a system: the `Rule
54' qubit chain, a model of cellular automaton introduced in the 1990s [Bobenko
et al., CMP 158, 127 (1993)], recently advertised as the simplest
representative of interacting integrable systems. Physically, the logarithmic
bound originates from the fact that the dynamics of the models is mapped onto
the one of stable quasiparticles that scatter elastically; the possibility of
generalizing this scenario to other interacting integrable systems is briefly
discussed.Comment: 4+16 pages, 2+6 figures. Substantial rewriting of the presentation.
As published in PR
The isolated Heisenberg magnet as a quantum time crystal
We demonstrate analytically and numerically that the paradigmatic model of
quantum magnetism, the Heisenberg XXZ spin chain, does not relax to
stationarity and hence constitutes a genuine time crystal that does not rely on
external driving or coupling to an environment. We trace this phenomenon to the
existence of extensive dynamical symmetries and find their frequency to be a
no-where continuous (fractal) function of the anisotropy parameter of the
chain. We discuss how the ensuing persistent oscillations that violate one of
the most fundamental laws of physics could be observed experimentally and
identify potential metrological applications.Comment: Main text: 5 pages, 2 figures; Supplementary: 4 pages, 1 figure. New
version contains study of stability to integrability breakin
Quasilocal charges in integrable lattice systems
We review recent progress in understanding the notion of locality in
integrable quantum lattice systems. The central concept are the so-called
quasilocal conserved quantities, which go beyond the standard perception of
locality. Two systematic procedures to rigorously construct families of
quasilocal conserved operators based on quantum transfer matrices are outlined,
specializing on anisotropic Heisenberg XXZ spin-1/2 chain. Quasilocal conserved
operators stem from two distinct classes of representations of the auxiliary
space algebra, comprised of unitary (compact) representations, which can be
naturally linked to the fusion algebra and quasiparticle content of the model,
and non-unitary (non-compact) representations giving rise to charges,
manifestly orthogonal to the unitary ones. Various condensed matter
applications in which quasilocal conservation laws play an essential role are
presented, with special emphasis on their implications for anomalous transport
properties (finite Drude weight) and relaxation to non-thermal steady states in
the quantum quench scenario.Comment: 51 pages, 3 figures; review article for special issue of JSTAT on
non-equilibrium dynamics in integrable systems; revised version to appear in
JSTA
Super-diffusion in one-dimensional quantum lattice models
We identify a class of one-dimensional spin and fermionic lattice models
which display diverging spin and charge diffusion constants, including several
paradigmatic models of exactly solvable strongly correlated many-body dynamics
such as the isotropic Heisenberg spin chains, the Fermi-Hubbard model, and the
t-J model at the integrable point. Using the hydrodynamic transport theory, we
derive an analytic lower bound on the spin and charge diffusion constants by
calculating the curvature of the corresponding Drude weights at half filling,
and demonstrate that for certain lattice models with isotropic interactions
some of the Noether charges exhibit super-diffusive transport at finite
temperature and half filling.Comment: 4 pages + appendices, v2 as publishe
Rigorous bounds on dynamical response functions and time-translation symmetry breaking
Dynamical response functions are standard tools for probing local physics
near the equilibrium. They provide information about relaxation properties
after the equilibrium state is weakly perturbed. In this paper we focus on
systems which break the assumption of thermalization by exhibiting persistent
temporal oscillations. We provide rigorous bounds on the Fourier components of
dynamical response functions in terms of extensive or local dynamical
symmetries, i.e. extensive or local operators with periodic time dependence.
Additionally, we discuss the effects of spatially inhomogeneous dynamical
symmetries. The bounds are explicitly implemented on the example of an
interacting Floquet system, specifically in the integrable Trotterization of
the Heisenberg XXZ model.Comment: 18 pages, 3 figures, slightly revised version with new reference
-deformed conformal field theories out of equilibrium
We consider the out-of-equilibrium transport in -deformed
(1+1)-dimension conformal field theories (CFTs). The theories admit two
disparate approaches, integrability and holography, which we make full use of
in order to compute the transport quantities, such as the the exact
non-equilibrium steady state currents. We find perfect agreements between the
results obtained from these two methods, which serve as the first checks of the
-deformed holographic correspondence from the dynamical standpoint.
It turns out that integrability also allows us to compute the momentum
diffusion, which is given by a universal formula. We also remark on an
intriguing connection between the -deformed CFTs and reversible
cellular automata.Comment: v1: 6 pages, 1 figure. v2: typos corrected, v3: Fig. 1 corrected,
published versio
Diffusion from Convection
We introduce non-trivial contributions to diffusion constant in generic
many-body systems arising from quadratic fluctuations of ballistically
propagating, i.e. convective, modes. Our result is obtained by expanding the
current operator in the vicinity of equilibrium states in terms of powers of
local and quasi-local conserved quantities. We show that only the second-order
terms in this expansion carry a finite contribution to diffusive spreading. Our
formalism implies that whenever there are at least two coupled modes with
degenerate group velocities, the system behaves super-diffusively, in
accordance with the non-linear fluctuating hydrodynamics theory. Finally, we
show that our expression saturates the exact diffusion constants in quantum and
classical interacting integrable systems, providing a general framework to
derive these expressions.Comment: 26 pages, 1 figur
Thermal transport in -deformed conformal field theories: from integrability to holography
In this paper we consider the energy and momentum transport in
(1+1)-dimension conformal field theories (CFTs) that are deformed by an
irrelevant operator , using the integrability based generalized
hydrodynamics, and holography. The two complementary methods allow us to study
the energy and momentum transport after the in-homogeneous quench, derive the
exact non-equilibrium steady states (NESS) and calculate the Drude weights and
the diffusion constants. Our analysis reveals that all of these quantities
satisfy universal formulae regardless of the underlying CFT, thereby
generalizing the universal formulae for these quantities in pure CFTs. As a
sanity check, we also confirm that the exact momentum diffusion constant agrees
with the conformal perturbation. These fundamental physical insights have
important consequences for our understanding of the -deformed CFTs.
First of all, they provide the first check of the -deformed
/ correspondence from the dynamical standpoint.
And secondly, we are able to identify a remarkable connection between the
-deformed CFTs and reversible cellular automata.Comment: v1: 18 pages, 3 figures. v2: 20 pages, 3 figures, substantially
improved results including a general derivation of the momentum diffusion
constant. v3: Fig. 1 corrected, explanations improved. Published versio