Alexander Seel, Tanaya Bhattacharyya, Frank Göhmann, Andreas Klümper
By considering the one-particle and two-particle scattering data of the spin-1/2 Heisenberg chain at T=0 we derive a continuum limit relating the spin chain to the 1D Bose gas. Applying this limit to the quantum transfer matrix approach of the Heisenberg chain we obtain expressions for the correlation functions of the Bose gas at arbitrary temperatures.
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We consider the K-body local correlations in the (repulsive) 1D Bose gas for general K, both at finite size and in the thermodynamic limit. Concerning the latter we develop a multiple integral formula which applies for arbitrary states of the system with a smooth distribution of Bethe roots, including the ground state and finite temperature Gibbs-states. In the cases K<=4 we perform the explicit factorization of the multiple integral. In the case of K=3 we obtain the recent result of Kormos et.al., whereas our formula for K=4 is new. Numerical results are presented as well.
We present a Gaudin-like determinant expression for overlaps of $q$-raised Néel states with Bethe states of the spin-1/2 XXZ chain in the non-zero magnetization sector. The former is constructed by applying global $U_q(sl_2)$ spin raising operators to the Néel state, the ground state of the antiferromagnetic Ising chain. The formulas presented are derived from recently-obtained results for the overlap of the Néel state with XXZ Bethe states. The determinants as well as their prefactors can be evaluated in the scaling limit of the XXZ spin chain to the Lieb-Liniger Bose gas. Within this limit a…
We present a novel and open-source implementation of the worm algorithm, which is an algorithm to simulate Bose-Hubbard and sign-positive spin models using a path integral representation of the partition function. The code can deal with arbitrary lattice structures and assumes spin-exchange terms, or bosonic hopping amplitudes, between nearest-neighbor sites, and local or nearest-neighbor interactions of the density-density type. We explicitly demonstrate the near-linear scaling of the algorithm with respect to the system volume and the inverse temperature and analyze the autocorrelation times…
We investigate the large-distance asymptotic behavior of the static density-density and field-field correlation functions in the one-dimensional Bose gas at finite temperature. The asymptotic expansions of the Bose gas correlators are obtained performing a specific continuum limit in the similar low-temperature expansions of the longitudinal and transversal correlation functions of the XXZ spin chain. In the lattice system the correlation lengths are computed as ratios of the largest and next-largest eigenvalues of the XXZ spin chain quantum transfer matrix. In both cases, lattice and continuu…
Algebraic contraction is proposed to realize mappings between models Hamiltonians. This transformation contracts the algebra of the degrees of freedom underlying the Hamiltonian. The rigorous mapping between the anisotropic $XXZ$ Heisenberg model, the Quantum Phase Model, and the Bose Hubbard Model is established as the contractions of the algebra $u(2)$ underlying the dynamics of the $XXZ$ Heisenberg model.
A number of conjectures have been given recently concerning the connection between the antiferromagnetic XXZ spin chain at $Δ= - \frac12$ and various symmetry classes of alternating sign matrices. Here we use the integrability of the XXZ chain to gain further insight into these developments. In doing so we obtain a number of new results using Baxter's $Q$ function for the XXZ chain for periodic, twisted and open boundary conditions. These include expressions for the elementary symmetric functions evaluated at the groundstate solution of the Bethe roots. In this approach Schur functions play a …
The magnetization process of the spin-1/2 antiferromagnetic XXZ model with Ising-like anisotropy in the ground state is investigated. We show numerically that the Ising-like XXZ models on square and cubic lattices show a first-order phase transition at some critical magnetic field. We estimate the value of the critical field and the magnetization jump on the basis of the Maxwell construction. The magnetization jump in the Ising-limit is investigated by means of perturbation theory. Based on our numerical results, we briefly discuss the phase diagram of the extended Bose-Hubbard model in the ha…
Quantum integrable systems, such as the interacting Bose gas in one dimension and the XXZ quantum spin chain, have an extensive number of local conserved quantities that endow them with exotic thermalization and transport properties. We discuss recently introduced hydrodynamic approaches for such integrable systems from the viewpoint of kinetic theory and extend the previous works by proposing a numerical scheme to solve the hydrodynamic equations for finite times and arbitrary locally equilibrated initial conditions. We then discuss how such methods can be applied to describe non-equilibrium …
Thermodynamics of the spin 1/2 XXZ model is studied in the critical regime using the quantum transfer matrix (QTM) approach. We find functional relations indexed by the Takahashi-Suzuki numbers among the fusion hierarchy of the QTM's (T-system) and their certain combinations (Y-system). By investigating analyticity of the latter, we derive a closed set of non-linear integral equations which characterize the free energy and the correlation lengths for both <sigma_j^{+} sigma_i^{-}> and <sigma_j^{z} sigma_i^{z}> at any finite temperatures. Concerning the free energy, they exactly coincide with T…
We specialize a recently-proposed determinant formula for the overlap of the zero-momentum Néel state with Bethe states of the spin-1/2 XXZ chain to the case of an odd number of downturned spins, showing that it is still of "Gaudin-like" form, similar to the case of an even number of down spins. We generalize this result to the overlap of $q$-raised Néel states with parity-invariant Bethe states lying in a nonzero magnetization sector. The generalized determinant expression can then be used to derive the corresponding determinants and their prefactors in the scaling limit to the Lieb-Liniger (…
Following our previous work [PRL 113 (2014) 09020] we present here a detailed comparison of the quench action approach and the predictions of the generalized Gibbs ensemble, with the result that while the quench action formalism correctly captures the steady state, the GGE does not give a correct description of local short-distance correlation functions. We extend our studies to include another initial state, the so-called q-dimer state. We present important details of our construction, including new results concerning exact overlaps for the dimer and q-dimer states, and we also give an exact …
We demonstrate the universal properties of dissipative Tomonaga-Luttinger (TL) liquids by calculating correlation functions and performing finite-size scaling analysis of a non-Hermitian XXZ spin chain as a prototypical model in one-dimensional open quantum many-body systems. Our analytic calculation is based on effective field theory with bosonization, finite-size scaling approach in conformal field theory, and the Bethe-ansatz solution. Our numerical analysis is based on the density-matrix renormalization group generalized to non-Hermitian systems (NH-DMRG). We uncover that the model in the …
The rates at which energy and particle densities move to equalize arbitrarily large temperature and chemical potential differences in an isolated quantum system have an emergent thermodynamical description whenever energy or particle current commutes with the Hamiltonian. Concrete examples include the energy current in the 1D spinless fermion model with nearest-neighbor interactions (XXZ spin chain), energy current in Lorentz-invariant theories or particle current in interacting Bose gases in arbitrary dimension. Even far from equilibrium, these rates are controlled by state functions, which w…
We study ergodicity breaking in the clean Bose-Hubbard chain for small hopping strength. We see the existence of a non-ergodic regime by means of indicators as the half-chain entanglement entropy of the eigenstates, the average level spacing ratio, {the properties of the eigenstate-expectation distribution of the correlation and the scaling of the Inverse Participation Ratio averages.} We find that this ergodicity breaking {is different from many-body localization} because the average half-chain entanglement entropy of the eigenstates obeys volume law. This ergodicity breaking appears unrelate…
We study the dynamics of condensate formation in an inhomogeneous trapped Bose gas with a positive interatomic scattering length. We take into account both the nonequilibrium kinetics of the thermal cloud and the Hartree-Fock mean-field effects in the condensed and the noncondensed parts of the gas. Our growth equations are solved numerically by assuming that the thermal component behaves ergodically and that the condensate, treated within the Thomas-Fermi approximation, grows adiabatically. Our simulations are in good qualitative agreement with experiment, however important discrepancies conc…
We extend the self-consistent Hartree-Fock-Popov calculations by Nikuni et al. [Phys. Rev. Lett. 84, 5868 (2000)] concerning the Bose-Eistein condensation of magnons in TlCuCl3 to include a realistic dispersion of the excitations. The result for the critical field as a function of temperature behaves as Hc(T)-Hc(0) T^{3/2} below 2K but deviates from this simple power-law at higher temperature and is in very good agreement with the experimental results. The specific heat is computed as a function of temperature for different values of the magnetic field. It shows a lambda-like shape at the tran…
The well-known results concerning a dilute Bose gas with the short-range repulsive interaction should be reconsidered due to a thermodynamic inconsistency of the method being basic to much of the present understanding of this subject. The aim of our paper is to propose a new way of treating the dilute Bose gas with an arbitrary strong interaction. Using the reduced density matrix of the second order and a variational procedure, this way allows us to escape the inconsistency mentioned and operate with singular potentials of the Lennard-Jones type. The derived expansion of the condensate depleti…
We study the Rényi entanglement entropy and the Shannon mutual information for a class of spin-1/2 quantum critical XXZ chains with random coupling constants which are partially correlated. In the XX case, distinctly from the usual uncorrelated random case where the system is governed by an infinite-disorder fixed point, the correlated-disorder chain is governed by finite-disorder fixed points. Surprisingly, we verify that, although the system is not conformally invariant, the leading behavior of the Rényi entanglement entropies are similar to those of the clean (no randomness) conformally inv…
In this letter we continue the investigation of finite XXZ spin chains with periodic boundary conditions and odd number of sites, initiated in paper \cite{S}. As it turned out, for a special value of the asymmetry parameter $Δ=-1/2$ the Hamiltonian of the system has an eigenvalue, which is exactly proportional to the number of sites $E=-3N/2$. Using {\sc Mathematica} we have found explicitly the corresponding eigenvectors for $N \le 17$. The obtained results support the conjecture of paper \cite{S} that this special eigenvalue corresponds to the ground state vector. We make a lot of conjecture…
The well-known results concerning a dilute Bose gas with the short-range repulsive interaction should be reconsidered due to a thermodynamic inconsistency of the method being basic to much of the present understanding of this subject and nonrelevant behaviour of the pair distribution function at small boson separations. The aim of our paper is to propose a new way of treating the dilute Bose gas with an arbitrary strong interaction. Using the reduced density matrix of the second order and a variational procedure, this way allows us to escape the inconsistency mentioned and operate with singula…
Some basic concepts concerning systems of identical particles are discussed in the framework of a realist interpretation, where the wave function is the quantum object and |psi(r)|^2 d^3r is the probability that the wave function causes an effect about the point r. The topics discussed include the role of Hilbert-space labels, wave-function variables and wave-function parameters, the distinction between permutation and renaming, the reason for symmetrizing the wave function, the reason for antisymmetric wave functions, the spin-statistics theorem, the correction term -k lnN! in the entropy, th…
In this paper, the particles of quantum gases, that is, bosons and fermions are regarded as g-ons which obey fractional exclusion statistics. With this point of departure the thermostatistical relations concerning the Bose and Fermi systems are unified under the g-on formulation where a fractal approach is adopted. The fractal inspired entropy, the partition function, distribution function, the thermodynamics potential and the total number of g-ons have been found for a grand canonical g-on system. It is shown that from the g-on formulation; by a suitable choice of the parameters of the nonext…
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