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Title: Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition

Abstract

We show that the peak which can be observed in fidelity susceptibility around the Berezinskii-Kosterlitz-Thouless transition is shifted from the quantum critical point (QCP) at J c to J* in the gapped phase by a value | J*– J c| = B 2/36, where B 2 is a transition width controlling the asymptotic form of the correlation length ξ~exp(– B/√| JJ c|) in that phase. This is in contrast to the conventional continuous QCP where the maximum is an indicator of the position of the critical point. The shape of the peak is universal, emphasizing the close connection between fidelity susceptibility and the correlation length. Here, we support those arguments with numerical matrix product state simulations of the one-dimensional Bose-Hubbard model in the thermodynamic limit, where the broad peak is located at J* = 0.212 that is significantly different from J c = 0.3048(3). In the spin-3/2 XXZ model the shift from J c = 1 to J* = 1.0021 is small but the narrow universal peak is much more pronounced over the nonuniversal background.

Authors:
ORCiD logo [1];  [2];  [2]; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Jagiellonian Univ., Krakow (Poland)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1572334
Alternate Identifier(s):
OSTI ID: 1558143
Report Number(s):
LA-UR-19-25340
Journal ID: ISSN 2469-9950; PRBMDO
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 100; Journal Issue: 8; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING; Mathematics; Material Science

Citation Formats

Cincio, Lukasz, Rams, Marek Maria, Dziarmaga, Jacek Piotr, and Zurek, Wojciech Hubert. Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition. United States: N. p., 2019. Web. doi:10.1103/PhysRevB.100.081108.
Cincio, Lukasz, Rams, Marek Maria, Dziarmaga, Jacek Piotr, & Zurek, Wojciech Hubert. Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition. United States. doi:10.1103/PhysRevB.100.081108.
Cincio, Lukasz, Rams, Marek Maria, Dziarmaga, Jacek Piotr, and Zurek, Wojciech Hubert. Mon . "Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition". United States. doi:10.1103/PhysRevB.100.081108.
@article{osti_1572334,
title = {Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition},
author = {Cincio, Lukasz and Rams, Marek Maria and Dziarmaga, Jacek Piotr and Zurek, Wojciech Hubert},
abstractNote = {We show that the peak which can be observed in fidelity susceptibility around the Berezinskii-Kosterlitz-Thouless transition is shifted from the quantum critical point (QCP) at Jc to J* in the gapped phase by a value |J*–Jc| = B2/36, where B2 is a transition width controlling the asymptotic form of the correlation length ξ~exp(–B/√|J–Jc|) in that phase. This is in contrast to the conventional continuous QCP where the maximum is an indicator of the position of the critical point. The shape of the peak is universal, emphasizing the close connection between fidelity susceptibility and the correlation length. Here, we support those arguments with numerical matrix product state simulations of the one-dimensional Bose-Hubbard model in the thermodynamic limit, where the broad peak is located at J* = 0.212 that is significantly different from Jc = 0.3048(3). In the spin-3/2 XXZ model the shift from Jc = 1 to J* = 1.0021 is small but the narrow universal peak is much more pronounced over the nonuniversal background.},
doi = {10.1103/PhysRevB.100.081108},
journal = {Physical Review B},
number = 8,
volume = 100,
place = {United States},
year = {2019},
month = {8}
}

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