TY - JOUR
T1 - Energy-twisted boundary condition and response in one-dimensional quantum many-body systems
AU - Nakai, Ryota
AU - Guo, Taozhi
AU - Ryu, Shinsei
N1 - Funding Information:
We thank Vir Bulchandani, Hosho Katsura, Jonah Kudler-Flam, Kentaro Nomura, and Kiyohide Nomura for discussions. R.N. is supported by JSPS KAKENHI Grant No. JP17K17604 and JST CREST Grant No. JPMJCR18T2. S.R. is supported by the National Science Foundation under Award No. DMR-2001181, and by a Simons Investigator Grant from the Simons Foundation (Award No. 566116). This work is supported by the Gordon and Betty Moore Foundation through Grant No. GBMF8685 toward the Princeton theory program. This work was performed in part at Aspen Center for Physics, which is supported by National Science Foundation Grant No. PHY-1607611. This work was partially supported by a grant from the Simons Foundation.
Publisher Copyright:
© 2022 American Physical Society.
PY - 2022/10/15
Y1 - 2022/10/15
N2 - Thermal transport in condensed matter systems is traditionally formulated as a response to a background gravitational field. In this work, we seek a twisted-boundary-condition formalism for thermal transport in analogy to the U(1) twisted boundary condition for electrical transport. Specifically, using the transfer matrix formalism, we introduce what we call the energy-twisted boundary condition, and study the response of the system to the boundary condition. As specific examples, we obtain the thermal Meissner stiffness of (1+1)-dimensional CFT, the Ising model, and disordered fermion models. We also identify the boost deformation of integrable systems as a bulk counterpart of the energy-twisted boundary condition. We show that the boost deformation of the free fermion chain can be solved explicitly by solving the inviscid Burgers equation. We also discuss the boost deformation of the XXZ model, and its nonlinear thermal Drude weights, by studying the boost-deformed Bethe ansatz equations.
AB - Thermal transport in condensed matter systems is traditionally formulated as a response to a background gravitational field. In this work, we seek a twisted-boundary-condition formalism for thermal transport in analogy to the U(1) twisted boundary condition for electrical transport. Specifically, using the transfer matrix formalism, we introduce what we call the energy-twisted boundary condition, and study the response of the system to the boundary condition. As specific examples, we obtain the thermal Meissner stiffness of (1+1)-dimensional CFT, the Ising model, and disordered fermion models. We also identify the boost deformation of integrable systems as a bulk counterpart of the energy-twisted boundary condition. We show that the boost deformation of the free fermion chain can be solved explicitly by solving the inviscid Burgers equation. We also discuss the boost deformation of the XXZ model, and its nonlinear thermal Drude weights, by studying the boost-deformed Bethe ansatz equations.
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U2 - 10.1103/PhysRevB.106.155128
DO - 10.1103/PhysRevB.106.155128
M3 - Article
AN - SCOPUS:85140616906
SN - 2469-9950
VL - 106
JO - Physical Review B
JF - Physical Review B
IS - 15
M1 - 155128
ER -