Our general interest is in self-consistent-field (scf) theories of disordered fermions. They generate physically relevant subensembles (``scf ensembles'') within a given Altland-Zirnbauer class. We are motivated to investigate such ensembles (i) by the possibility to discover new fixed points due to (long-range) interactions; (ii) by analytical scf theories that rely on partial self-consistency approximations awaiting a numerical validation; and (iii) by the overall importance of scf theories for the understanding of complex interaction-mediated phenomena in terms of effective single-particle pictures. In this paper we present an efficient, parallelized implementation solving scf problems with spatially local fields by applying a kernel-polynomial approach. Our first application is the Boguliubov-deGennes theory of the attractive- $U$ Hubbard model in the presence of on-site disorder; the sc fields are the particle density $n(\mathbf{r})$ and the gap function $\mathrm{\ensuremath{\Delta}}(\mathbf{r})$. For this case, we reach system sizes unprecedented in earlier work. They allow us to study phenomena emerging at scales substantially larger than the lattice constant, such as the interplay of multifractality and interactions or the formation of superconducting islands. For example, we observe that the coherence length exhibits a nonmonotonic behavior with increasing disorder strength already at moderate $U$ . With respect to methodology our results are important because we establish that partial self-consistency (``energy-only'') schemes as typically employed in analytical approaches tend to miss qualitative physics such as island formation.Our general interest is in self-consistent-field (scf) theories of disordered fermions. They generate physically relevant subensembles (``scf ensembles'') within a given Altland-Zirnbauer class. We are motivated to investigate such ensembles (i) by the possibility to discover new fixed points due to (long-range) interactions; (ii) by analytical scf theories that rely on partial self-consistency approximations awaiting a numerical validation; and (iii) by the overall importance of scf theories for the understanding of complex interaction-mediated phenomena in terms of effective single-particle pictures. In this paper we present an efficient, parallelized implementation solving scf problems with spatially local fields by applying a kernel-polynomial approach. Our first application is the Boguliubov-deGennes theory of the attractive-$U$ Hubbard model in the presence of on-site disorder; the sc fields are the particle density $n(\mathbf{r})$ and the gap function $\mathrm{\ensuremath{\Delta}}(\mathbf{r})$. For this case, we reach system sizes unprecedented in earlier work. They allow us to study phenomena emerging at scales substantially larger than the lattice constant, such as the interplay of multifractality and interactions or the formation of superconducting islands. For example, we observe that the coherence length exhibits a nonmonotonic behavior with increasing disorder strength already at moderate $U$. With respect to methodology our results are important because we establish that partial self-consistency (``energy-only'') schemes as typically employed in analytical approaches tend to miss qualitative physics such as island formation.

arXiv:1903.10395Physical review. B./Physical review. BApr 13, 202016 citations

a Study of the Disordered Boson Systems

Lizeng Zhang

Jan 1, 19900 citations

On the density field description of a boson system

Chan Hong-Mo, Jean G. Valatin

Il Nuovo CimentoJan 1, 196113 citations

Dielectric response of the degenerate plasma of charged bosons in static-local-field approximations

Sergio Conti, M. L. Chiofalo, Monica Tosi

The dielectric screening function epsilon (k, omega ) of the fluid of charged bosom at zero temperature is evaluated in a range of low-to-intermediate coupling strength, in view of recent data on static screening and fluid structure from quantum Monte Carlo methods. Correlations beyond the random phase approximation are included within a class of approximations which are well known for the electron fluid, i.e. by introducing a frequency-independent local field factor to be determined through self-consistency requirements connecting various aspects of the physics contained in the dielectric function. The static dielectric function epsilon (k,0) is negative over a range of wavenumbers at all values of the density, leading to oscillatory screening of a foreign charge and to an effective long-range attraction between equi-charged impurities. Quantitative agreement with the Monte Carlo data on static screening is achieved by imposing self-consistency on the compressibility of the fluid in addition to self-consistency on the pair distribution function. Good agreement is also obtained on the pair distribution function and the correlation energy. Within the present class of approximations, the dispersion relation of longitudinal excitations takes the Feynman form, starting at the plasma frequency with a negative dispersion coefficient and going through a minimum before ending at the single-particle recoil frequency.The dielectric screening function epsilon (k, omega ) of the fluid of charged bosom at zero temperature is evaluated in a range of low-to-intermediate coupling strength, in view of recent data on static screening and fluid structure from quantum Monte Carlo methods. Correlations beyond the random phase approximation are included within a class of approximations which are well known for the electron fluid, i.e. by introducing a frequency-independent local field factor to be determined through self-consistency requirements connecting various aspects of the physics contained in the dielectric function. The static dielectric function epsilon (k,0) is negative over a range of wavenumbers at all values of the density, leading to oscillatory screening of a foreign charge and to an effective long-range attraction between equi-charged impurities. Quantitative agreement with the Monte Carlo data on static screening is achieved by imposing self-consistency on the compressibility of the fluid in addition to self-consistency on the pair distribution function. Good agreement is also obtained on the pair distribution function and the correlation energy. Within the present class of approximations, the dispersion relation of longitudinal excitations takes the Feynman form, starting at the plasma frequency with a negative dispersion coefficient and going through a minimum before ending at the single-particle recoil frequency.

Journal of Physics Condensed MatterOct 17, 199418 citations

The strongly-interacting spinless boson fluid: Statistical thermodynamics of the fluid surface

Clive A. Croxton

Physics Letters AOct 1, 19721 citation

Hydrodynamic Cooperons in Electron Fluids: Schwinger--Keldysh Derivation and Quantum Corrections to Magnetoresistance

Alberto Cortijo

We develop a Schwinger--Keldysh effective theory for quantum-interference corrections in a two-dimensional electron system in the hydrodynamic regime. Starting from the clean hydrodynamic fixed point, we introduce a minimal random-friction disorder model that generates a finite momentum-relaxation time within the self-consistent Born approximation. The disorder-averaged theory then allows us to construct a hydrodynamic Cooperon and to compute the associated self-energy corrections to the collective modes. Conservation laws protect the density and momentum sectors, so that the leading quantum-coherence correction is forced into the spin-two stress sector. The associated stress self-energy renormalizes the shear viscosity and modifies both the Gurzhi response and its low-field magnetohydrodynamic signatures.We develop a Schwinger--Keldysh effective theory for quantum-interference corrections in a two-dimensional electron system in the hydrodynamic regime. Starting from the clean hydrodynamic fixed point, we introduce a minimal random-friction disorder model that generates a finite momentum-relaxation time within the self-consistent Born approximation. The disorder-averaged theory then allows us to construct a hydrodynamic Cooperon and to compute the associated self-energy corrections to the collective modes. Conservation laws protect the density and momentum sectors, so that the leading quantum-coherence correction is forced into the spin-two stress sector. The associated stress self-energy renormalizes the shear viscosity and modifies both the Gurzhi response and its low-field magnetohydrodynamic signatures.

arXiv:2605.26226May 25, 20260 citations

U

Hubbard model in the presence of on-site disorder; the sc fields are the particle density

n(\mathbf{r})

and the gap function $\mathrm{\ensuremath{\Delta}}(\mathbf{r})$. For this case, we reach system sizes unprecedented in earlier work. They allow us to study phenomena emerging at scales substantially larger than the lattice constant, such as the interplay of multifractality and interactions or the formation of superconducting islands. For example, we observe that the coherence length exhibits a nonmonotonic behavior with increasing disorder strength already at moderate

U

. With respect to methodology our results are important because we establish that partial self-consistency (``energy-only'') schemes as typically employed in analytical approaches tend to miss qualitative physics such as island formation.