The equilibrium landscape of the Heisenberg spin chain

Abstract

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.

Current operators in integrable spin chains: lessons from long range deformations

“…Typically the amplitudes decay exponentially with the range. The quasi-local operators play an essential role in the description of the Generalized Gibbs Ensemble of Heisenberg spin chain and related models [17,18,19,20,21,22]. There a commuting set of quasi-local charges is derived from the fused transfer matrices.…”

Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

“…A natural way to test such concepts is to consider evolution of the physical system after some parameters of the Hamiltonian have been rapidly changed -this is the so-called quantum quench setup [1][2][3][4]. After a long time a quenched integrable system equilibrates to a steady state that can be described in the quench action formalism [5,6] or by a complete generalized Gibbs ensemble (GGE) [7][8][9][10][11][12][13][14].…”

Analytical results for the low-temperature Drude weight of the XXZ spin chain

“…In addition, there exist, however, also quasi-local charges for γ = nπ/m ∈ Q with n, m coprime obtained from transfer matrices when a general highest weight representation in auxiliary space is chosen instead of the standard spin-1/2 representation [9,31,32]. Completeness of the set of local and quasi-local conserved charges is believed to be a consequence of the underlying quantum group [35], and taking all the symmetries into account turns the Mazur bound in Eq. (2.4) into an equality [34].…”