Vanishing spin stiffness in the spin-12Heisenberg chain for any nonzero temperature

Abstract

Whether at zero spin density m = 0 and finite temperatures T > 0 the spin stiffness of the spin-1/2 XXX chain is finite or vanishes remains an unsolved and controversial issue, as different approaches yield contradictory results. Here we provide an exact upper bound on the stiffness within a canonical ensemble at any fixed value of spin density m and show that it is proportional to m 2 L in the thermodynamic limit of chain length L → ∞, for any finite, nonzero temperature. Moreover, we explicitly compute the stiffness at m = 0 and confirm that it vanishes. This allows us to exactly exclude the possibility of ballistic transport within the canonical ensemble for T > 0.

Finite-temperature transport in one-dimensional quantum lattice models

“…An alternative calculation based on a spinon-antispinon basis was presented in (Benz et al, 2005). The thermodynamic Bethe-ansatz approach predicts that D (171) For ∆ = 1, a second Bethe-ansatz-based calculation (Carmelo et al, 2015) concludes in favor of D (S) w = 0, in agreement with GHD (Ilievski et al, 2018).…”

“…Several open questions remain in the regime ∆ > 1 as well. While analytical calculation based on certain assumptions (Carmelo et al, 2015) conclude in favor of D (S) w = 0 at T > 0, a strict proof is still missing. An exact lower bound to the diffusion constant was obtained and shown to be finite, ruling out subdiffusion (Ilievski et al, 2018).…”

Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures

“…In particular, Prosen constructed quasi-local conserved quantities [27,30,36] to show analytically that D c is finite throughout the gapless phase (excluding the isotropic point); quantitative numbers can be obtained, e.g., using the real-time density matrix renormalization group (DMRG) [29,37] or dynamical typicality [31]. Whether or not the Drude weight is finite for an isotropic chain is still debated [28,29,31,38].…”

Microscopic Origin of Ideal Conductivity in Integrable Quantum Models

“…Although this has been shown to hold almost universally [2], spin and charge transport in system with unbroken particle-hole symmetries instead show normal (or even anomalous) diffusion [3][4][5][6][7]. Despite long efforts, the question whether the spin Drude weight in the isotropic Heisenberg spin chain at finite temperature and at half filling is precisely zero is still vividly debated [8][9][10], with a number of conflicting statements spread in the literature: while the prevailing opinion is that the spin Drude weight vanishes [9][10][11][12][13][14][15], other studies reach the opposite conclusion [16][17][18][19][20][21]. As the question is inherently related to asymptotic timescales in thermodynamically large systems, numerical approaches -ranging from exact diagonalization to DMRG [9,14,15,17,18,21,22] -are insufficient to offer the conclusive and unambiguous answer.In this Letter, we rigorously settle the issue by closely examining the underlying particle content which emerges in thermodynamically large systems, and combine it with symmetry-based arguments to lay down the complete microscopic background of ideal (dissipationless) conductivity.…”