Low temperature phases of interacting fermions in two dimensions

We consider the Gross-Neveu model with a continuous chiral symmetry in two and three spacetime dimensions at zero and finite temperature. In order to study long-range phase coherence, we construct an effective low-energy Lagrangian for the phase $θ$ . This effective Lagrangian is used to show that the fermionic two-particle correlation function at finite temperature decays algebraically in 2+1 dimensions and exponentially in 1+1 dimensions.We consider the Gross-Neveu model with a continuous chiral symmetry in two and three spacetime dimensions at zero and finite temperature. In order to study long-range phase coherence, we construct an effective low-energy Lagrangian for the phase $θ$. This effective Lagrangian is used to show that the fermionic two-particle correlation function at finite temperature decays algebraically in 2+1 dimensions and exponentially in 1+1 dimensions.

arXiv:hep-th/0506261Jun 30, 20051 citation

Interacting Fermions in 2 Dimensions

Vincent Rivasseau

Lecture notes in physicsJan 1, 20060 citations

The coupled SYK model at finite temperature

Xiao-Liang Qi

Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS2 dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS2 geometry. This geometry is an “eternal wormhole" because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function.Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS2 dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS2 geometry. This geometry is an “eternal wormhole" because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function.

Jul 4, 202333 citations

Renormalization group study of interacting fermions at finite temperatures

Adrian A. Drǎgulescu, Adrian Neagu

Jan 1, 19950 citations

The coupled SYK model at finite temperature

Xiao-Liang Qi, Pengfei Zhang

Abstract Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS2 dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS2 geometry. This geometry is an “eternal wormhole” because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function.Abstract Sachdev-Ye-Kitaev (SYK) model, which describes N randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS2 dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS2 geometry. This geometry is an “eternal wormhole” because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the q dependence of the spectral function.

arXiv:2003.03916Journal of High Energy PhysicsMay 26, 202027 citations

Fermi Liquids in Two Dimensions

WORLD SCIENTIFIC eBooksMar 1, 20080 citations

θ

. This effective Lagrangian is used to show that the fermionic two-particle correlation function at finite temperature decays algebraically in 2+1 dimensions and exponentially in 1+1 dimensions.