Related papers: Boundary driven $XYZ$ chain: Exact inhomogeneous t…
Many low-dimensional materials are well described by integrable one-dimensional models such as the Hubbard model of electrons or the Heisenberg model of spins. However, the small perturbations to these models required to describe real…
We consider $\mathfrak{so}_4$ invariant matrix product states (MPS) in the $\mathfrak{so}_6$ symmetric integrable spin chain and prove their integrability. These MPS appear as fuzzy three-sphere solutions of matrix models with…
We consider the tricritical Ising model on a strip or cylinder under the integrable perturbation by the thermal $\phi_{1,3}$ boundary field. This perturbation induces five distinct renormalization group (RG) flows between Cardy type…
We show that all zero energy eigenstates of an arbitrary $m$--state quantum spin chain Hamiltonian with nearest neighbor interaction in the bulk and single site boundary terms, which can also describe the dynamics of stochastic models, can…
Taking the isotropic limit in a recent representation theoretic construction of Baxter's Q-operators for the XXZ model with quasi-periodic boundary conditions we obtain new results for the XXX model. We show that quasi-periodic boundary…
In this note, we derive the spectrum of the infinite quantum XXZ spin chain with domain wall boundary conditions. The eigenstates are constructed as limits of Bethe states for the finite XXZ spin chain with quantum sl(2) invariant boundary…
The off-diagonal Bethe ansatz method is generalized to the integrable model associated with the $sp(4)$ (or $C_2$) Lie algebra. By using the fusion technique, we obtain the complete operator product identities among the fused transfer…
We present a convergence result for infinite products of stochastic matrices with positive diagonals. We regard infinity of the product to the left. Such a product converges partly to a fixed matrix if the minimal positive entry of each…
In this paper we apply the formalism of translation invariant (continuous) matrix product states in the thermodynamic limit to $(1+1)$ dimensional critical models. Finite bond dimension bounds the entanglement entropy and introduces an…
The Bethe ansatz equations of the 1-D Hubbard model under open boundary conditions are systematically derived by diagonalizing the inhomogeneous transfer matrix of the XXX model with open boundaries. Through the finite-size correction, we…
We derive bounds for the entanglement of a spin with an (adjacent and non-adjacent) interval of spins in an arbitrary pure finitely correlated state (FCS) on a chain of spins of any magnitude. Finitely correlated states are otherwise known…
In this paper, we prove the off-shell equation satisfied by the transfer matrix associated with the XXZ spin-$\frac12$ chain on the segment with two generic integrable boundaries acting on the Bethe vector. The essential step is to prove…
We study a collection of polar self-propelled particles confined to a long two-dimensional channel. We write the coupled hydrodynamic equations of motion for density and polarisation order parameter. At two confined boundaries, density is…
Just as matrix product states represent ground states of one-dimensional quantum spin systems faithfully, continuous matrix product states (cMPS) provide faithful representations of the vacuum of interacting field theories in one spatial…
The thermodynamic limits of the XYZ spin chain with periodic or twisted boundary conditions are studied. By using the technique of characterizing the eigenvalue of the transfer matrix by the $T-Q$ relation and by the zeros of the associated…
We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression…
We construct exact steady states of unitary non-equilibrium time evolution in the gapless XXZ spin-1/2 chain where integrability preserves ballistic spin transport at long-times. We characterize the quasi-local conserved quantities…
Integrable systems possess stable families of quasiparticles, which are composite objects (bound states) of elementary excitations. Motivated by recent quantum computer experiments, we investigate bound-state transport in the spin-$1/2$…
We study the large deviations of sums of correlated random variables described by a matrix product ansatz, which generalizes the product structure of independent random variables to matrices whose non-commutativity is the source of…
We present an integral formula for the density matrix of a finite segment of the infinitely long spin-1/2 XXZ chain. This formula is valid for any temperature and any longitudinal magnetic field.