The flow of the low energy eigenstates of a $U_q[sl(2|1)]$ superspin chain with alternating fundamental ($3$) and dual ($\bar{3}$) representations is studied as function of a twist angle determining the boundary conditions. The finite size spectrum is characterized in terms of scaling dimensions and quasi momenta representing the two families of commuting transfer matrices for the model which are even and odd under the interchange $3\leftrightarrow \bar{3}$, respectively. Based on the extrapolation of our finite size data we find that under a variation of the boundary conditions from periodic to antiperiodic for the fermionic degrees of freedom levels from the continuous part of the spectrum flow into discrete levels and vice versa.
Based on the exact solution of the eigenvalue problem for the $U_q[sl(2|1)]$ vertex model built from alternating 3-dimensional fundamental and dual representations by means of the algebraic Bethe ansatz we investigate the ground state and low energy excitations of the corresponding mixed superspin chain for deformation parameter $q=\exp(-iγ/2)$. The model has a line of critical points with central charge $c=0$ and continua of conformal dimensions grouped into sectors with $γ$-dependent lower edges for $0\leγ<π/2$. The finite size scaling behaviour is consistent with a low energy effective theo…
This paper is concerned with the investigation of the massless regime of an integrable spin chain based on the quantum group deformation of the $OSp(3|2)$ superalgebra. The finite-size properties of the eigenspectra are computed by solving the respective Bethe ansatz equations for large system sizes allowing us to uncover the low-lying critical exponents. We present evidences that critical exponents appear to be built in terms of composites of anomalous dimensions of two Coulomb gases with distinct radii and the exponents associated to $Z(2)$ degrees of freedom. This view is supported by the f…
We construct a family of integrable vertex model based on the typical four-dimensional representations of the quantum group deformation of the Lie superalgebra $sl(2|1)$. Upon alternation of such a representation with its dual this model gives rise to a mixed superspin Hamiltonian with local interactions depending on the representation parameter $\pm b$ and the deformation parameter $γ$. As a subsector this model contains integrable vertex models with ordinary symmetries for twisted boundary conditions. The thermodynamic limit and low energy properties of the mixed superspin chain are studied …
The low energy spectrum of a spin chain with $OSp(3|2)$ supergroup symmetry is studied based on the Bethe ansatz solution of the related vertex model. This model is a lattice realization of intersecting loops in two dimensions with loop fugacity $z=1$ which provides a framework to study the critical properties of the unusual low temperature Goldstone phase of the $O(N)$ sigma model for $N=1$ in the context of an integrable model. Our finite-size analysis provides strong evidence for the existence of continua of scaling dimensions, the lowest of them starting at the ground state. Based on our d…
Yang-Baxter integrable vertex models with a generic $\mathbb{Z}_2$-staggering can be expressed in terms of composite $\mathbb{R}$-matrices given in terms of the elementary $R$-matrices. Similarly, integrable open boundary conditions can be constructed through generalized reflection algebras based on these objects and their representations in terms of composite boundary matrices $\mathbb{K}^\pm$. We show that only two types of staggering yield a local Hamiltonian with integrable open boundary conditions in this approach. The staggering in the underlying model allows for a second hierarchy of co…
The antiferromagnetic critical point of the Potts model on the square lattice was identified by Baxter as a staggered integrable six-vertex model. In this work, we investigate the integrable structure of this model. It enables us to derive some new properties, such as the Hamiltonian limit of the model, an equivalent vertex model, and the structure resulting from the Z_2 symmetry. Using this material, we discuss the low-energy spectrum, and relate it to geometrical excitations. We also compute the critical exponents by solving the Bethe equations for a large lattice width N. The results confir…
We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine $D_2^2$ Lie algebra. Using the known relations between the staggered six-vertex model and the antiferromagnetic Potts model, this mapping allows us to study the latter model using tools from integrability. We show that there is a simple interpretation of one of the known K-matrices of the $D_2^2$ model in terms of Temperley-Lieb algebra generators, and use this to present an integrable Hamiltonian that turns out to be in the same universality class as the antiferromagn…
In this work we analyze the simultaneous emergence of diffusive energy transport and local thermalization in a nonequilibrium one-dimensional quantum system, as a result of integrability breaking. Specifically, we discuss the local properties of the steady state induced by thermal boundary driving in a XXZ spin chain with staggered magnetic field. By means of efficient large-scale matrix product simulations of the equation of motion of the system, we calculate its steady state in the long-time limit.We start by discussing the energy transport supported by the system, finding it to be ballistic…
It was previously established that the critical staggered XXZ spin chain provides a lattice regularization of the black hole CFT. We reconsider the continuum limit of this spin chain with the exact method of non-linear integral equations (NLIEs), paying particular attention to the effects of a singular integration kernel. With the help of the NLIEs, we rederive the continuous black hole spectrum, but also numerically match the density of states of the spin chain with that of the CFT, which is a new result. Finally, we briefly discuss the integrable structure of the black hole CFT and the ident…
We investigate the dynamics of two Jordan Wigner solvable models, namely, the one dimensional chain of hard-core bosons (HCB) and the one-dimensional transverse field Ising model under coin-toss like aperiodically driven staggered on-site potential and the transverse field, respectively. It is demonstrated that both the models heat up to the infinite temperature ensemble for a minimal aperiodicity in driving. Consequently, in the case of the HCB chain, we show that the initial current generated by the application of a twist vanishes in the asymptotic limit for any driving frequency. For the tr…
We discuss a general procedure to construct an integrable real-time trotterization of interacting lattice models. As an illustrative example we consider a spin-$1/2$ chain, with continuous time dynamics described by the isotropic ($XXX$) Heisenberg Hamiltonian. For periodic boundary conditions local conservation laws are derived from an inhomogeneous transfer matrix and a boost operator is constructed. In the continuous time limit these local charges reduce to the known integrals of motion of the Heisenberg chain. In a simple Kraus representation we also examine the nonequilibrium setting, whe…
We use the concept of typicality to study the real-time dynamics of spin and energy currents in spin-1/2 models in one dimension and at nonzero temperatures. These chains are the integrable XXZ chain and a nonintegrable modification due to the presence of a staggered magnetic field oriented in z direction. In the framework of linear response theory, we numerically calculate autocorrelation functions by propagating a single pure state, drawn at random as a typical representative of the full statistical ensemble. By comparing to small-system data from exact diagonalization (ED) and existing shor…
We use non-equilibrium steady states to study the effect of dissipation-assisted operator evolution (DAOE) on the scaling behavior of transport in one-dimensional spin chains. We consider three models in the XXZ family: the XXZ model with staggered anisotropy, which is chaotic; XXZ model with no external field and tunable interaction, which is Bethe ansatz integrable and (in the zero interaction limit) free fermion integrable; and the disordered XY model, which is free-fermion integrable and Anderson localized. We find evidence that DAOE's effect on transport is controlled by its effect on the…
Open-boundary integrable quantum circuits with different geometries
Instituto Galego de Física de Altas Enerxías (IGFAE), and Departamento de Física de Partículas, Universidade de Santiago de Compostela（加利西亚高能物理研究所，圣地亚哥德孔波斯特拉大学粒子物理系）；Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院物理系）；Department of Mathematical Sciences, Durham University（杜伦大学数学科学系）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）
Non-compact Conformal Field Theories (CFTs) are central to several aspects of string theory and condensed matter physics. They are characterised, in particular, by the appearance of a continuum of conformal dimensions. Surprisingly, such CFTs have been identified as the continuum limits of lattice models with a finite number of degrees of freedom per site. However, results have so far been restricted to the case of periodic boundary conditions, precluding the exploration via lattice models of aspects of non-compact boundary CFTs and the corresponding D-brane constructions. The present paper fo…
