Zero-frequency transport properties of one-dimensional spin-12systems

Abstract

We report a detailed analysis of the Drude weights for both thermal and spin transport in one dimensional spin-1/2 systems by means of exact diagonalization and analytic approaches at finite temperatures. Transport properties are studied first for the integrable XXZ model and second for various nonintegrable systems such as the dimerized chain, the frustrated chain, and the spin ladder. We compare our results obtained by exact diagonalization and mean-field theory with those of the Bethe ansatz, bosonization and other numerical studies in the case of the anisotropic Heisenberg model both in the gapless and gapped regime. In particular, we find indications that the Drude weight for spin transport is finite in the thermodynamic limit for the isotropic chain. For the nonintegrable models, a finite-size analysis of the numerical data for the Drude weights is presented covering the entire parameter space of the dimerized and frustrated chain. We also discuss which conclusions can be drawn from bosonization regarding the question of whether the Drude weights are finite or not. One of our main results is that the Drude weights vanish in the thermodynamic limit for nonintegrable models. I. INTRODUCTIONDue to their relevance for modeling the magnetic properties of several quasi-one-dimensional materials, dimerized and frustrated spin-1/2 chains and ladders are models of great and current interest. Recently, growing experimental evidence has been found that magnetic excitations can contribute significantly to the thermal conductivity of various quasi-one and quasi-two-dimensional materials [1][2][3][4][5][6][7][8][9][10][11] . Stimulated by these observations, many theoretical activities have addressed the issue of heat transport in one-dimensional spin systems [12][13][14][15][16][17][18][19][20][21][22] . While spin transport has been a topic of numerous theoretical investigations , the theory of thermal transport is less well understood. One of the key questions is to understand under which conditions transport is ballistic, i.e., dissipationless. The criterion for this is the existence of a singularity at zero frequency in the real part of the conductivity. Therefore, one is interested in the integrated weight of this singularity -the so called Drude weight -in the thermodynamic limit. The appearance of a nonzero Drude weight is often ascribed to the influence of conservation laws on transport properties 30,38,43,46,47 . For example, in the case of the Heisenberg chain the energy-current operator is conserved 30,48 implying a nonzero thermal Drude weight at all temperatures. Another widely discussed and related issue is the difference between transport in integrable models compared to nonintegrable ones 15,17,20,27,33,41,43 . The purpose of the present paper is to provide a systematic study of both the Drude weight for spin and thermal transport at finite temperatures by means of exact diagonalization on finite systems and analytic methods. The dependence on exchange coupling anisotropy, frustration and dimerization ...

Sudden expansion of Mott insulators in one dimension

“…The same applies to hard-core bosons on a ladder, equivalent to an XX spin-1/2 model. In fact, existing studies of spin transport for spin ladders indicate (i) the absence of a ballistic contribution 32 and (ii) diffusive spreading of density perturbations with a finite background density 67,69 (for examples of ballistic dynamics on certain spin ladders, see the recent work byŽnidarič in Ref. 38).…”

“…Moreover, hard-core bosons on a ladder are equivalent to XX spin-1/2 ladders, connecting our work to studies of spin transport in 1D quantum magnets. 19,32,38,39 ACKNOWLEDGMENT We thank N. Andrei, C. Bolech, and M. Rigol for fruitful discussions, and we thank S. Thwaite, M. Rigol, and J. P. from real-time calculations using the DMRG method with a discarded weight η 10 −4 . In all our data, we used a time step tJ = 1/16 and different values of N max to verify that the results are independent of N max (N max denotes the maximal number of bosons per site used in DMRG calculations).…”

“…Nonetheless, there are many intriguing experimental results, in particular for low-dimensional quantum magnets, [29][30][31] that are speculated to be related to the existence of such conservation laws for the underlying spin Hamiltonians. In contrast, many nonintegrable 1D models seem to exhibit dynamics that are compatible with diffusion, [32][33][34][35][36] although several exceptions have also been identified. [37][38][39] In this work, we consider the sudden expansion of interacting particles into a homogeneous lattice, sketched in Fig.…”

Heat conductivity of the spin-Peierls compounds TiOCl and TiOBr

“…In particular, transition metal oxides provide a rich playground for studying novel phenomena, arising from the interplay between lattice, orbital, spin, and charge degrees of freedom. The recent discovery of a substantial magnetic heat conductivity mag in one-dimensional ͑1D͒ quantum spin systems, [1][2][3][4][5][6][7][8][9][10][11] together with the theoretical prediction of ballistic transport in 1D S =1/ 2 Heisenberg chains, [12][13][14] has caused intense experimental and theoretical research on the behavior of these systems. The best experimental realizations of S =1/ 2 systems showing magnetic heat transport are up to now found among copper oxides ͑cu-prates͒ such as the spin chains SrCuO 2 1,3,5,8 Characteristic for the cuprate chain systems is a Cu 3d 9 configuration which gives rise to S =1/ 2 and a large exchange coupling J / k B Ϸ 2000 K along the chain/ladder direction.…”

Coexistence of Diffusive and Ballistic Transport in a Simple Spin Ladder

“…[4]. For recent studies of transport in spin ladders see [6][7][8][9][10][11]. With rapidly progressing experimental cold atoms techniques [12], transport properties of Fermi gases [13] as well as of the Hubbard model [14] have actually been measured.…”