Universal behavior at continuous phase transitions is encoded in long-wavelength fixed-point theories controlled by dimensionality and symmetries. It is a central question for which systems this universal behavior and the underlying long-wavelength description can be captured by a noninteracting theory allowing for analytical and accurate predictions. In this work we provide a systematic procedure for obtaining the best noninteracting fermionic description of a quantum phase transition through fermionic Gaussian states. We demonstrate the performance of our procedure for the interacting long-range transverse-field Ising chain. This formulation reduces the problem to a self-consistent Euler equation that yields a critical line in close agreement with independent numerical benchmarks, while its singular momentum structure provides analytic predictions for continuously varying critical properties. Yet exact diagonalization shows that Gaussian-state fidelity to the exact ground state is poorest, and non-Gaussianity strongest, near the transition. Thus, accurate predictions for critical properties can emerge from the Gaussian variational description even where its microscopic wave-function approximation is weakest.Universal behavior at continuous phase transitions is encoded in long-wavelength fixed-point theories controlled by dimensionality and symmetries. It is a central question for which systems this universal behavior and the underlying long-wavelength description can be captured by a noninteracting theory allowing for analytical and accurate predictions. In this work we provide a systematic procedure for obtaining the best noninteracting fermionic description of a quantum phase transition through fermionic Gaussian states. We demonstrate the performance of our procedure for the interacting long-range transverse-field Ising chain. This formulation reduces the problem to a self-consistent Euler equation that yields a critical line in close agreement with independent numerical benchmarks, while its singular momentum structure provides analytic predictions for continuously varying critical properties. Yet exact diagonalization shows that Gaussian-state fidelity to the exact ground state is poorest, and non-Gaussianity strongest, near the transition. Thus, accurate predictions for critical properties can emerge from the Gaussian variational description even where its microscopic wave-function approximation is weakest.

quant-pharXiv:2610.26246Oct 20, 20260 citations

Quantum critical phenomena in spin systems

Subir Sachdev A

Jan 1, 19970 citations

Dynamical critical behavior of long-range spin models

Paraj Titum, Mohammad F. Maghrebi

Bulletin of the American Physical SocietyMar 5, 20190 citations

Quantum Monte Carlo simulations of the BCS-BEC crossover at finite temperature

Aurel Bulgac, Joaquín E. Drut, Piotr Magierski

The quantum Monte Carlo method for spin- $\frac{1}{2}$ fermions at finite temperature is formulated for dilute systems with an $s$ -wave interaction. The motivation and the formalism are discussed along with descriptions of the algorithm and various numerical issues. We report on results for the energy, entropy, and chemical potential as a function of temperature. We give upper bounds on the critical temperature ${T}_{c}$ for the onset of superfluidity, obtained by studying the finite-size scaling of the condensate fraction. All of these quantities were computed for couplings around the unitary regime in the range $\ensuremath{-}0.5\ensuremath{\leqslant}{({k}_{F}a)}^{\ensuremath{-}1}\ensuremath{\leqslant}0.2$, where $a$ is the $s$ -wave scattering length and ${k}_{F}$ is the Fermi momentum of a noninteracting gas at the same density. In all cases our data are consistent with normal Fermi gas behavior above a characteristic temperature ${T}_{0}>{T}_{c}$ , which depends on the coupling and is obtained by studying the deviation of the caloric curve from that of a free Fermi gas. For ${T}_{c}<T<{T}_{0}$ we find deviations from normal Fermi gas behavior that can be attributed to pairing effects. Low-temperature results for the energy and the pairing gap are shown and compared with Green-function Monte Carlo results by other groups.The quantum Monte Carlo method for spin-$\frac{1}{2}$ fermions at finite temperature is formulated for dilute systems with an $s$-wave interaction. The motivation and the formalism are discussed along with descriptions of the algorithm and various numerical issues. We report on results for the energy, entropy, and chemical potential as a function of temperature. We give upper bounds on the critical temperature ${T}_{c}$ for the onset of superfluidity, obtained by studying the finite-size scaling of the condensate fraction. All of these quantities were computed for couplings around the unitary regime in the range $\ensuremath{-}0.5\ensuremath{\leqslant}{({k}_{F}a)}^{\ensuremath{-}1}\ensuremath{\leqslant}0.2$, where $a$ is the $s$-wave scattering length and ${k}_{F}$ is the Fermi momentum of a noninteracting gas at the same density. In all cases our data are consistent with normal Fermi gas behavior above a characteristic temperature ${T}_{0}>{T}_{c}$, which depends on the coupling and is obtained by studying the deviation of the caloric curve from that of a free Fermi gas. For ${T}_{c}<T<{T}_{0}$ we find deviations from normal Fermi gas behavior that can be attributed to pairing effects. Low-temperature results for the energy and the pairing gap are shown and compared with Green-function Monte Carlo results by other groups.

arXiv:0803.3238Physical Review AAug 21, 2008173 citations

Critical behavior of an isotropic spin system

Anthony John Guttmann, G S Joyce, Colin J. Thompson

Physics Letters AFeb 1, 197212 citations

Quantum criticality near the Stoner transition in a system of two tunnel-coupled quantum dots with spin-orbit coupling

Oleksandr Zelyak, Ganpathy N. Murthy

We study a system of two tunnel-coupled quantum dots with the first dot containing interacting electrons (described by the universal Hamiltonian) not subject to spin-orbit coupling whereas the second contains noninteracting electrons subject to spin-orbit coupling. We focus on describing the behavior of the system near the Stoner transition. Close to the critical point quantum fluctuations become important and the system enters a quantum-critical regime. The large- $N$ approximation allows us to calculate physical quantities reliably even in this strongly fluctuating regime. In particular, we find a scaling function to describe the crossover of the quasiparticle decay rate between the renormalized Fermi-liquid regime and the quantum-critical regime.We study a system of two tunnel-coupled quantum dots with the first dot containing interacting electrons (described by the universal Hamiltonian) not subject to spin-orbit coupling whereas the second contains noninteracting electrons subject to spin-orbit coupling. We focus on describing the behavior of the system near the Stoner transition. Close to the critical point quantum fluctuations become important and the system enters a quantum-critical regime. The large-$N$ approximation allows us to calculate physical quantities reliably even in this strongly fluctuating regime. In particular, we find a scaling function to describe the crossover of the quasiparticle decay rate between the renormalized Fermi-liquid regime and the quantum-critical regime.

arXiv:0906.1838Physical Review BNov 12, 20097 citations

The quantum Monte Carlo method for spin-

\frac{1}{2}

fermions at finite temperature is formulated for dilute systems with an

s

-wave interaction. The motivation and the formalism are discussed along with descriptions of the algorithm and various numerical issues. We report on results for the energy, entropy, and chemical potential as a function of temperature. We give upper bounds on the critical temperature

{T}_{c}

for the onset of superfluidity, obtained by studying the finite-size scaling of the condensate fraction. All of these quantities were computed for couplings around the unitary regime in the range $\ensuremath{-}0.5\ensuremath{\leqslant}{({k}_{F}a)}^{\ensuremath{-}1}\ensuremath{\leqslant}0.2$, where

a

is the

s

-wave scattering length and

{k}_{F}

is the Fermi momentum of a noninteracting gas at the same density. In all cases our data are consistent with normal Fermi gas behavior above a characteristic temperature

{T}_{0}>{T}_{c}

, which depends on the coupling and is obtained by studying the deviation of the caloric curve from that of a free Fermi gas. For

{T}_{c}<T<{T}_{0}

we find deviations from normal Fermi gas behavior that can be attributed to pairing effects. Low-temperature results for the energy and the pairing gap are shown and compared with Green-function Monte Carlo results by other groups.

N

approximation allows us to calculate physical quantities reliably even in this strongly fluctuating regime. In particular, we find a scaling function to describe the crossover of the quasiparticle decay rate between the renormalized Fermi-liquid regime and the quantum-critical regime.