7 research outputs found
Current mean values in the XYZ model
The XYZ model is an integrable spin chain which has an infinite set of
conserved charges, but it lacks a global -symmetry. We consider the
current operators, which describe the flow of the conserved quantities in this
model. We derive an exact result for the current mean values, valid for any
eigenstate in a finite volume with periodic boundary conditions. This result
can serve as a basis for studying the transport properties of this model within
Generalized Hydrodynamics.Comment: 27 page
Matrix product symmetries and breakdown of thermalization from hard rod deformations
We construct families of exotic spin-1/2 chains using a procedure called
``hard rod deformation''. We treat both integrable and non-integrable examples.
The models possess a large non-commutative symmetry algebra, which is generated
by matrix product operators with fixed small bond dimension. The symmetries
lead to Hilbert space fragmentation and to the breakdown of thermalization. As
an effect, the models support persistent oscillations in non-equilibrium
situations. Similar symmetries have been reported earlier in integrable models,
but here we show that they also occur in non-integrable cases.Comment: v2: references correcte
Current operators in integrable models: A review
We consider the current operators of one dimensional integrable models. These
operators describe the flow of the conserved charges of the models, and they
play a central role in Generalized Hydrodynamics. We present the key statements
about the mean currents in finite volume and in the thermodynamic limit, and we
review the various proofs of the exact formulas. We also present a few new
results in this review. New contributions include a computation of the currents
of the Heisenberg spin chains using the string hypothesis, and simplified
formulas in the thermodynamic limit. We also discuss implications of our
results for the asymptotic behaviour of dynamical correlation functions.Comment: 38 pages, to be submitted to the special issue of Journal of
Statistical Mechanics on Emergent Hydrodynamics in Integrable Many-body
System
Current operators in Bethe Ansatz and Generalized Hydrodynamics: An exact quantum/classical correspondence
Generalized Hydrodynamics is a recent theory that describes large scale
transport properties of one dimensional integrable models. It is built on the
(typically infinitely many) local conservation laws present in these systems,
and leads to a generalized Euler type hydrodynamic equation. Despite the
successes of the theory, one of its cornerstones, namely a conjectured
expression for the currents of the conserved charges in local equilibrium has
not yet been proven for interacting lattice models. Here we fill this gap, and
compute an exact result for the mean values of current operators in Bethe
Ansatz solvable systems, valid in arbitrary finite volume. Our exact formula
has a simple semi-classical interpretation: the currents can be computed by
summing over the charge eigenvalues carried by the individual bare particles,
multiplied with an effective velocity describing their propagation in the
presence of the other particles. Remarkably, the semi-classical formula remains
exact in the interacting quantum theory, for any finite number of particles and
also in the thermodynamic limit. Our proof is built on a form factor expansion
and it is applicable to a large class of quantum integrable models.Comment: 26 page
Sublattice entanglement in an exactly solvable anyonlike spin ladder
We introduce an integrable spin ladder model and study its exact solution, correlation functions, and entanglement properties. The model supports two particle types (corresponding to the even and odd sublattices), such that the scattering phases are constants: Particles of the same type scatter as free fermions, whereas the interparticle phase shift is a constant tuned by an interaction parameter. Therefore, the spin ladder bears similarities with anyonic models. We present exact results for the spectrum and correlation functions, and we study the sublattice entanglement by numerical means
Sub-lattice entanglement in an exactly solvable anyon-like spin ladder
We introduce an integrable spin ladder model and study its exact solution,
correlation functions, and entanglement properties. The model supports two
particle types (corresponding to the even and odd sub-lattices), such that the
scattering phases are constants: particles of the same type scatter as free
fermions, whereas the inter-particle phase shift is a constant tuned by an
interaction parameter. Therefore, the spin ladder bears similarities with
anyonic models. We present exact results for the spectrum and correlation
functions, and we study the sub-lattice entanglement by numerical means.Comment: 5 pages, 4 figures, v2: references adde
An integrable spin chain with Hilbert space fragmentation and solvable real time dynamics
We revisit the so-called folded XXZ model, which was treated earlier by two independent research groups. We argue that this spin-1/2 chain is one of the simplest quantum integrable models, yet it has quite remarkable physical properties. The particles have constant scattering lengths, which leads to a simple treatment of the exact spectrum and the dynamics of the system. The Hilbert space of the model is fragmented, leading to exponentially large degeneracies in the spectrum, such that the exponent depends on the particle content of a given state. We provide an alternative derivation of the Hamiltonian and the conserved charges of the model, including a new interpretation of the so-called "dual model" considered earlier. We also construct a non-local map that connects the model with the Maassarani-Mathieu spin chain, also known as the SU(3) XX model. We consider the exact solution of the model with periodic and open boundary conditions, and also derive multiple descriptions of the exact thermodynamics of the model. We consider quantum quenches of different types. In one class of problems the dynamics can be treated relatively easily: we compute an example for the real time dependence of a local observable. In another class of quenches the degeneracies of the model lead to the breakdown of equilibration, and we argue that they can lead to persistent oscillations. We also discuss connections with the - and hard rod deformations known from Quantum Field Theories