Speaker: Ryota Nakai (Kyushu University)

Date & Time: 10am, Aug 1, 2022.

Title: Twisted boundary condition and thermal transport in one-dimensional quantum many-body systems

Abstract:

Thermal transport is of particular importance in probing charge-neutral particles such as Majorana fermions, which are the subject of intensive study [1,2]. Theoretically, thermal transport cannot be analyzed on the same footing as electrical transport since the driving force, temperature bias, is a statistical force. However, it is well known that there is a parallelism between electrical and thermal transport, in which a gravitational force is used to effectively represent the temperature bias [3], just as the electric potential for charged particles works in the same way as the chemical potential.

In this talk, I will discuss another type of parallelism by introducing what we call the energy-twisted boundary condition [4]. This boundary condition is shown to be intimately related to thermal analogues of the Drude weight (charge stiffness) and the Meissner stiffness, just as the U(1) twisted boundary condition is to electrical stiffnesses [5,6,7]. The formulation of implementing the twist will be explained for CFT and the one-dimensional transverse Ising model.

The bulk counterpart of the energy-twisted boundary condition is identified with the boost deformation, which is a sort of integrable deformations [8]. I will discuss the boost deformation of the free fermion, and the linear and nonlinear thermal Drude weights of the XXZ spin chain calculated via the boost deformation of the Bethe ansatz equations.

[1] M. Banerjee et al., Nature 559, 205 (2018).

[2] Y. Kasahara et al., Nature 559, 227 (2018).

[3] J. M. Luttinger, Phys. Rev. 135, A1505 (1964).

[4] R. Nakai, T. Guo, and S. Ryu, arXiv:2206.00641.

[5] W. Kohn, Phys. Rev. 133, A171 (1964).

[6] J. T. Edwards and D. J. Thouless, J. Phys. C: Solid State Phys. 5, 807 (1972).

[7] D. J. Thouless, Phys. Rev. Lett. 39, 1167 (1977).

[8] T. Bargheer, N. Beisert, and F. Loebbert, J. Phys. A: Math. Theor. 42, 285205 (2009).