Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

High Temperature

Analytical contradictions of the fixed-node density matrix

Vladimir S. Filinov

Published Sep 1, 2014• 17 citations
Publisher

Abstract

Over the last decades the fixed-node method has been used for a numerical treatment of thermo-dynamic properties of strongly correlated Fermi systems. In this work correctness of the fixed-node method for ideal Fermi systems is analytically analyzed. It is shown that the fixed-node prescription of calculation of the density matrix leads to contradictions even for two ideal fermions. The main conclusion of this work is that the fixed-node method can not reproduce the fermion density matrices and should be considered as uncontrolled empirical approach in treatment of thermodynamics of Fermi systems.

DOI
10.1134/s0018151x14040105

Related papers

Analytical contradictions of the 'fixed - node' density matrices

Vladimir S. Filinov

Over the last decades the 'fixed-node method' has been used for a numerical treatment of thermodynamic properties of strongly correlated Fermi systems. In this work correctness of the 'fixed -node method' for ideal Fermi systems has been analytically analyzed. It is shown that the 'fixed-node' prescription of calculation of the density matrix leads to contradictions even for two ideal fermions. The main conclusion of this work is that the 'fixed-node method' can not reproduce the fermion density matrices and should be considered as uncontrolled empirical approach in treatment of thermodynamics of Fermi systems.

arXiv:1304.0216•Mar 31, 2013•0 citations

Cluster expansion for ideal Fermi systems in the `fixed-node approximation'

Vladimir S. Filinov

Over the last ten years the `fixed-node approximation', well known in the literature, has been widely used for a numerical treatment of thermodynamic properties of strongly correlated Fermi systems. Results of the direct path integral Monte Carlo simulation performed here show that the `fixed-node approximation' describes the thermodynamic properties of the strongly coupling fermions rather well at `weak and moderate' degeneracy. To analyse the reasons for the increasing difference between the `fixed-node approximation' and the results of direct path integral Monte Carlo simulations for highly degenerate fermions, the correctness of the `fixed-node approximation' for ideal Fermi systems has been analysed by analytical methods. A rigorous proof has been given of the fact that the exact Fermi function with index 3 / 2 describing the logarithm of the grand partition function of ideal fermions cannot be reproduced in the `fixed-node approximation', which means that the `fixed-node approximation' does not give the correct ideal Fermi gas limit.

Journal of Physics A Mathematical and General•Feb 19, 2001•20 citations

Jellium at finite temperature

Riccardo Fantoni

We adopt the fixed node restricted path integral Monte Carlo method within the ‘Worm algorithm’ to simulate Wigner's Jellium model at finite, non zero, temperatures using free-particle nodes of the density matrix. The new element is that we incorporate the Worm algorithm paradigm of Prokof'ev and Svistunov in the grand canonical ensemble in order to more efficiently handle the fermionic exchanges. We present results for the structure and thermodynamic properties of the ideal Fermi gas and three points for the interacting electron gas. We treat explicitly the case of the partially polarized electron gas.

arXiv:2110.07527•Molecular Physics•Oct 28, 2021•8 citations

One-body density matrix for quantum fluids in the diagonal limit

M. F. Flynn

Recent work has shown that the standard technique for solving the Fermi-hypernetted-chain equations violates certain diagonal limits of the one-body density matrix. The violations are traced to inconsistent treatment of elementary versus nonelementary cluster diagrams. A prescription for correcting this deficiency is proposed and applied to two strongly interacting Fermi quantum liquids, $^{3}\mathrm{He}$ and electron-spin-polarized deuterium.

Physical review. B, Condensed matter•Jan 1, 1986•10 citations

Superfluidity of a Fermi liquid from the viewpoint of a hierarchy of equations for reduced density matrices

В. А. Головко

The hierarchy of equations for reduced density matrices relevant to thermodynamic equilibrium with account taken of the spin obtained earlier is modified in order to describe the state of a Fermi system with a condensate. Although the procedure is to some extent analogous with the one carried out by the author earlier for a Bose liquid peculiarities relevant to Fermi statistics complicate considerably the treatment. As in the case of the Bose liquid the condensate phase can be superfluid as well as nonsuperfluid, the physical causes of superfluidity being identical. A new mechanism of fermion pairing that acts even in the case of a purely repulsive Hamiltonian is pointed out. Special attention is given to the thermodynamics of a superfluid Fermi system. The example of a hard-sphere system is used to find out the form of phase diagrams, the character of the phase transition to a condensate phase and the properties of the last. Noticeable dissimilarities from a Bose system with the same Hamiltonian are revealed. Application of the present approach to superconductivity is discussed as well.

Journal of Mathematical Physics•Mar 17, 2004•2 citations

Peculiarities of the momentum distribution functions of strongly correlated charged fermions

Alexander S. Larkin, Vladimir S. Filinov, В. Е. Фортов

Abstract New numerical version of the Wigner approach to quantum thermodynamics of strongly coupled systems of particles has been developed for extreme conditions, when analytical approximations based on different kinds of perturbation theories cannot be applied. An explicit analytical expression of the Wigner function has been obtained in linear and harmonic approximations. Fermi statistical effects are accounted for by effective pair pseudopotential depending on coordinates, momenta and degeneracy parameter of particles and taking into account Pauli blocking of fermions. A new quantum Monte-Carlo method for calculations of average values of arbitrary quantum operators has been developed. Calculations of the momentum distribution functions and the pair correlation functions of degenerate ideal Fermi gas have been carried out for testing the developed approach. Comparison of the obtained momentum distribution functions of strongly correlated Coulomb systems with the Maxwell–Boltzmann and the Fermi distributions shows the significant influence of interparticle interaction both at small momenta and in high energy quantum ‘tails’.

arXiv:1703.04448•Journal of Physics A Mathematical and Theoretical•Nov 7, 2017•24 citations
Over the last decades the fixed-node method has been used for a numerical treatment of thermo-dynamic properties of strongly correlated Fermi systems. In this work correctness of the fixed-node method for ideal Fermi systems is analytically analyzed. It is shown that the fixed-node prescription of calculation of the density matrix leads to contradictions even for two ideal fermions. The main conclusion of this work is that the fixed-node method can not reproduce the fermion density matrices and should be considered as uncontrolled empirical approach in treatment of thermodynamics of Fermi systems.
Over the last decades the 'fixed-node method' has been used for a numerical treatment of thermodynamic properties of strongly correlated Fermi systems. In this work correctness of the 'fixed -node method' for ideal Fermi systems has been analytically analyzed. It is shown that the 'fixed-node' prescription of calculation of the density matrix leads to contradictions even for two ideal fermions. The main conclusion of this work is that the 'fixed-node method' can not reproduce the fermion density matrices and should be considered as uncontrolled empirical approach in treatment of thermodynamics of Fermi systems.
Over the last ten years the `fixed-node approximation', well known in the literature, has been widely used for a numerical treatment of thermodynamic properties of strongly correlated Fermi systems. Results of the direct path integral Monte Carlo simulation performed here show that the `fixed-node approximation' describes the thermodynamic properties of the strongly coupling fermions rather well at `weak and moderate' degeneracy. To analyse the reasons for the increasing difference between the `fixed-node approximation' and the results of direct path integral Monte Carlo simulations for highly degenerate fermions, the correctness of the `fixed-node approximation' for ideal Fermi systems has been analysed by analytical methods. A rigorous proof has been given of the fact that the exact Fermi function with index 3 / 2 describing the logarithm of the grand partition function of ideal fermions cannot be reproduced in the `fixed-node approximation', which means that the `fixed-node approximation' does not give the correct ideal Fermi gas limit.
We adopt the fixed node restricted path integral Monte Carlo method within the ‘Worm algorithm’ to simulate Wigner's Jellium model at finite, non zero, temperatures using free-particle nodes of the density matrix. The new element is that we incorporate the Worm algorithm paradigm of Prokof'ev and Svistunov in the grand canonical ensemble in order to more efficiently handle the fermionic exchanges. We present results for the structure and thermodynamic properties of the ideal Fermi gas and three points for the interacting electron gas. We treat explicitly the case of the partially polarized electron gas.
Recent work has shown that the standard technique for solving the Fermi-hypernetted-chain equations violates certain diagonal limits of the one-body density matrix. The violations are traced to inconsistent treatment of elementary versus nonelementary cluster diagrams. A prescription for correcting this deficiency is proposed and applied to two strongly interacting Fermi quantum liquids, 3He^{3}\mathrm{He}3He and electron-spin-polarized deuterium.
The hierarchy of equations for reduced density matrices relevant to thermodynamic equilibrium with account taken of the spin obtained earlier is modified in order to describe the state of a Fermi system with a condensate. Although the procedure is to some extent analogous with the one carried out by the author earlier for a Bose liquid peculiarities relevant to Fermi statistics complicate considerably the treatment. As in the case of the Bose liquid the condensate phase can be superfluid as well as nonsuperfluid, the physical causes of superfluidity being identical. A new mechanism of fermion pairing that acts even in the case of a purely repulsive Hamiltonian is pointed out. Special attention is given to the thermodynamics of a superfluid Fermi system. The example of a hard-sphere system is used to find out the form of phase diagrams, the character of the phase transition to a condensate phase and the properties of the last. Noticeable dissimilarities from a Bose system with the same Hamiltonian are revealed. Application of the present approach to superconductivity is discussed as well.
Abstract New numerical version of the Wigner approach to quantum thermodynamics of strongly coupled systems of particles has been developed for extreme conditions, when analytical approximations based on different kinds of perturbation theories cannot be applied. An explicit analytical expression of the Wigner function has been obtained in linear and harmonic approximations. Fermi statistical effects are accounted for by effective pair pseudopotential depending on coordinates, momenta and degeneracy parameter of particles and taking into account Pauli blocking of fermions. A new quantum Monte-Carlo method for calculations of average values of arbitrary quantum operators has been developed. Calculations of the momentum distribution functions and the pair correlation functions of degenerate ideal Fermi gas have been carried out for testing the developed approach. Comparison of the obtained momentum distribution functions of strongly correlated Coulomb systems with the Maxwell–Boltzmann and the Fermi distributions shows the significant influence of interparticle interaction both at small momenta and in high energy quantum ‘tails’.