39 research outputs found
Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states
Using the Lindblad master equation approach, we investigate the structure of
steady-state solutions of open integrable quantum lattice models, driven far
from equilibrium by incoherent particle reservoirs attached at the boundaries.
We identify a class of boundary dissipation processes which permits to derive
exact steady-state density matrices in the form of graded matrix-product
operators. All the solutions factorize in terms of vacuum analogues of Baxter's
Q-operators which are realized in terms of non-unitary representations of
certain finite dimensional subalgebras of graded Yangians. We present a
unifying framework which allows to solve fermionic models and naturally
incorporates higher-rank symmetries. This enables to explain underlying
algebraic content behind most of the previously-found solutions.Comment: 28 pages, 5 figures + appendice
Exact steady state manifold of a boundary driven spin-1 Lai-Sutherland chain
We present an explicit construction of a family of steady state density
matrices for an open integrable spin-1 chain with bilinear and biquadratic
interactions, also known as the Lai-Sutherland model, driven far from
equilibrium by means of two oppositely polarizing Markovian dissipation
channels localized at the boundary. The steady state solution exhibits n+1 fold
degeneracy, for a chain of length n, due to existence of (strong) Liouvillian
U(1) symmetry. The latter can be exploited to introduce a chemical potential
and define a grand canonical nonequilibrium steady state ensemble. The matrix
product form of the solution entails an infinitely-dimensional representation
of a non-trivial Lie algebra (semidirect product of sl_2 and a non-nilpotent
radical) and hints to a novel Yang-Baxter integrability structure.Comment: 20 pages; version v2 as accepted by Nuclear Physics
The equilibrium landscape of the Heisenberg spin chain
We characterise the equilibrium landscape, the entire manifold of local
equilibrium states, of an interacting integrable quantum model. Focusing on the
isotropic Heisenberg spin chain, we describe in full generality two
complementary frameworks for addressing equilibrium ensembles: the functional
integral Thermodynamic Bethe Ansatz approach, and the lattice regularisation
transfer matrix approach. We demonstrate the equivalence between the two, and
in doing so clarify several subtle features of generic equilibrium states. In
particular we explain the breakdown of the canonical Y-system, which reflects a
hidden structure in the parametrisation of equilibrium ensembles.Comment: 31 pages, revised versio
Microscopic origin of ideal conductivity in integrable quantum models
Non-ergodic dynamical systems display anomalous transport properties. A
prominent example are integrable quantum systems, whose exceptional property
are diverging DC conductivities. In this Letter, we explain the microscopic
origin of ideal conductivity by resorting to the thermodynamic particle content
of a system. Using group-theoretic arguments we rigorously resolve the
long-standing controversy regarding the nature of spin and charge Drude weights
in the absence of chemical potentials. In addition, by employing a hydrodynamic
description, we devise an efficient computational method to calculate exact
Drude weights from the stationary currents generated in an inhomogeneous quench
from bi-partitioned initial states. We exemplify the method on the anisotropic
Heisenberg model at finite temperatures for the entire range of anisotropies,
accessing regimes which are out of reach with other approaches. Quite
remarkably, spin Drude weight and asymptotic spin current rates reveal a
completely discontinuous (fractal) dependence on the anisotropy parameter.Comment: 4 pages + Supplemental Materia
Popcorn Drude weights from quantum symmetry
Integrable models provide emblematic examples of non-ergodic phenomena. One
of their most distinguished properties are divergent zero-frequency
conductivities signalled by finite Drude weights. Singular conductivities owe
to long-lived quasiparticle excitations that propagate ballistically through
the system without any diffraction. The case of the celebrated quantum
Heisenberg chain, one of the best-studied many-body paradigms, turns out to be
particularly mysterious. About a decade ago, it was found that the spin Drude
weight in the critical phase of the model assumes an extraordinary, nowhere
continuous, dependence on the anisotropy parameter in the shape of a `popcorn
function'. This unprecedented discovery has been afterwards resolved at the
level of the underlying deformed quantum symmetry algebra which helps
explaining the erratic nature of the quasiparticle spectrum at commensurate
values of interaction anisotropy. This work is devoted to the captivating
phenomenon of discontinuous Drude weights, with the aim to give a broader
perspective on the topic by revisiting and reconciling various perspectives
from the previous studies. Moreover, it is argued that such an anomalous
non-ergodic feature is not exclusive to the integrable spin chain but can be
instead expected in a number of other integrable systems that arise from
realizations of the quantum group ,
specialized to unimodular values of the quantum deformation parameter . Our
discussion is framed in the context of gapless anisotropic quantum chains of
higher spin and the sine-Gordon quantum field theory in two space-time
dimensions.Comment: 58 pages. To appear in Focus Collection on "Hydrodynamics of
Low-Dimensional Quantum Systems'
Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
We outline a general formalism of hydrodynamics for quantum systems with
multiple particle species which undergo completely elastic scattering. In the
thermodynamic limit, the complete kinematic data of the problem consists of the
particle content, the dispersion relations, and a universal dressing
transformation which accounts for interparticle interactions. We consider
quantum integrable models and we focus on the one-dimensional fermionic Hubbard
model. By linearizing hydrodynamic equations, we provide exact closed-form
expressions for Drude weights, generalized static charge susceptibilities and
charge-current correlators valid on hydrodynamic scale, represented as integral
kernels operating diagonally in the space of mode numbers of thermodynamic
excitations. We find that, on hydrodynamic scales, Drude weights manifestly
display Onsager reciprocal relations even for generic (i.e. non-canonical)
equilibrium states, and establish a generalized detailed balance condition for
a general quantum integrable model. We present the first exact analytic
expressions for the general Drude weights in the Hubbard model, and explain how
to reconcile different approaches for computing Drude weights from the previous
literature.Comment: 4 pages + supplemental materia
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