We study the properties of a two-dimensional interacting electronic system in the presence of a staggered magnetic field. We find that metal-insulator transitions can be achieved at both zero and non-zero temperatures. A d-wave-like pseudogap is opened on the two-dimensional square Fermi surface. The staggered magnetic flux is found to suppress the antiferromagnetic order. When random fluctuations of the perfect staggered field are turned on and increased, a finite region of Fermi surface around (±π/2,±π/2) will be gradually formed as the bandwidth decreases. We also find that the assumed disturbed staggered field in our model can actually simulate the spin fluctuations occurring in the interacting system.We study the properties of a two-dimensional interacting electronic system in the presence of a staggered magnetic field. We find that metal-insulator transitions can be achieved at both zero and non-zero temperatures. A d-wave-like pseudogap is opened on the two-dimensional square Fermi surface. The staggered magnetic flux is found to suppress the antiferromagnetic order. When random fluctuations of the perfect staggered field are turned on and increased, a finite region of Fermi surface around (±π/2,±π/2) will be gradually formed as the bandwidth decreases. We also find that the assumed disturbed staggered field in our model can actually simulate the spin fluctuations occurring in the interacting system.

Journal of Physics Condensed MatterAug 8, 20000 citations

Thermodynamics of Small Fermi Systems: Quantum Statistical Fluctuations

P. Lebœuf, A.G. Monastra

arXiv:cond-mat/0110369Annals of PhysicsApr 1, 200218 citations

Phase Transitions in Fermi Systems

Paweł Jakubczyk

WORLD SCIENTIFIC eBooksJun 24, 20200 citations

A transition in the hole probability at finite temperature for free fermions in $d$ dimensionsA transition in the hole probability at finite temperature for free fermions in $d$ dimensions

Giuseppe Del Vecchio Del Vecchio, Pierre Le Doussal, Grégory Schehr

In a free Fermi gas at temperature $T$ much higher than the Fermi temperature one expects that the fluctuations of the number of particles in a given region has Poissonian/classical statistics. On the other hand at low temperature the Pauli exclusion principle leads to non trivial counting statistics. It is of great interest from a theoretical and experimental point of view to characterize the crossover between these two limits. Here we focus on the hole probability $P(R,T)$ , i.e. the probability that a region of size $R$ is devoid of particles, in dimension $d$ , and on the case of a spherical region of large radius $R$ . We show that at low temperature it takes the scaling form $P(R,T)\sim \exp\big[-(k_F R)^{d+1}Φ_d(u=2R\,T/k_F)\big],$ where $k_F$ is the Fermi momentum. By mapping the problem to an effective Coulomb gas, we compute exactly the scaling function $Φ_d(u)$ in any dimension. Remarkably, it exhibits a transition of order $\tfrac{3}{2}(d+1)$ at the universal critical value $u_c=2/π$ , signaling a sharp change in the mechanism of rare fluctuations, associated with the emergence of a macroscopic gap in the optimal density of the associated Coulomb gas. Our analytical predictions are supported by precise numerical evaluations of the corresponding Fredholm determinants.In a free Fermi gas at temperature $T$ much higher than the Fermi temperature one expects that the fluctuations of the number of particles in a given region has Poissonian/classical statistics. On the other hand at low temperature the Pauli exclusion principle leads to non trivial counting statistics. It is of great interest from a theoretical and experimental point of view to characterize the crossover between these two limits. Here we focus on the hole probability $P(R,T)$, i.e. the probability that a region of size $R$ is devoid of particles, in dimension $d$, and on the case of a spherical region of large radius $R$. We show that at low temperature it takes the scaling form $P(R,T)\sim \exp\big[-(k_F R)^{d+1}Φ_d(u=2R\,T/k_F)\big],$ where $k_F$ is the Fermi momentum. By mapping the problem to an effective Coulomb gas, we compute exactly the scaling function $Φ_d(u)$ in any dimension. Remarkably, it exhibits a transition of order $\tfrac{3}{2}(d+1)$ at the universal critical value $u_c=2/π$, signaling a sharp change in the mechanism of rare fluctuations, associated with the emergence of a macroscopic gap in the optimal density of the associated Coulomb gas. Our analytical predictions are supported by precise numerical evaluations of the corresponding Fredholm determinants.

arXiv:2605.05431May 6, 20260 citations

Phase transitions in Fermi systems

Börje Johansson

Jan 1, 19690 citations

A transition in the hole probability at finite temperature for free fermions in

d

dimensions

In a free Fermi gas at temperature

T

much higher than the Fermi temperature one expects that the fluctuations of the number of particles in a given region has Poissonian/classical statistics. On the other hand at low temperature the Pauli exclusion principle leads to non trivial counting statistics. It is of great interest from a theoretical and experimental point of view to characterize the crossover between these two limits. Here we focus on the hole probability

P(R,T)

, i.e. the probability that a region of size

R

is devoid of particles, in dimension

d

, and on the case of a spherical region of large radius

R

. We show that at low temperature it takes the scaling form

P(R,T)\sim \exp\big[-(k_F R)^{d+1}Φ_d(u=2R\,T/k_F)\big],

where

k_F

is the Fermi momentum. By mapping the problem to an effective Coulomb gas, we compute exactly the scaling function

Φ_d(u)

in any dimension. Remarkably, it exhibits a transition of order

\tfrac{3}{2}(d+1)

at the universal critical value

u_c=2/π

, signaling a sharp change in the mechanism of rare fluctuations, associated with the emergence of a macroscopic gap in the optimal density of the associated Coulomb gas. Our analytical predictions are supported by precise numerical evaluations of the corresponding Fredholm determinants.