Subsystem Rényi entropy of thermal ensembles for SYK-like models
Pengfei Zhang, Chunxiao Liu, Xiao Chen
Abstract
The Sachdev-Ye-Kitaev model is an N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>N</mml:mi> </mml:math> -modes fermionic model with infinite range random interactions. In this work, we study the thermal Rényi entropy for a subsystem of the SYK model using the path-integral formalism in the large- N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>N</mml:mi> </mml:math> limit. The results are consistent with exact diagonalization and can be well approximated by thermal entropy with an effective temperature when subsystem size M\leq N/2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>N</mml:mi> <mml:mi>/</mml:mi> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> . We also consider generalizations of the SYK model with quadratic random hopping term or U(1) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>U</mml:mi> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false" form="postfix">)</mml:mo> </mml:mrow> </mml:math> charge conservation.