Quantum Monte Carlo Approaches for Correlated Systems

Becca, Federico

doi:10.1017/9781316417041

Cited by 318 publications

(333 citation statements)

References 126 publications

Supporting

Mentioning

331

Contrasting

Order By: Relevance

“…where ϕ xn is given by the solution via Eqs. (3,4,6,7). The correlators obtained in that way are not necessarily equal to truncated functions that appear in the minimization equations Eq.…”

Section: Covariant Vs "Naive" Correlatormentioning

confidence: 99%

Covariant Bethe-Salpeter approximation in models of strongly correlated electron systems

Fan

Sun

et al. 2020

Phys. Rev. E

View full text Add to dashboard Cite

Strongly correlated electron systems are generally described by tight binding lattice Hamiltonians with strong local (on site) interactions, the most popular being the Hubbard model. Although the half filled Hubbard model can be simulated by Monte Carlo(MC), physically more interesting cases beyond half filling are plagued by the sign problem. One therefore should resort to other methods. It was demonstrated recently that a systematic truncation of the set of Dyson -Schwinger equations for correlators of the Hubbard, supplemented by a "covariant" calculation of correlators leads to a convergent series of approximants. The covariance preserves all the Ward identities among correlators describing various condensed matter probes. While first order (classical), second (Hartree -Fock or gaussian) and third (Cubic) covariant approximation were worked out, the fourth (quartic) seems too complicated to be effectively calculable in fermionic systems. It turns out that the complexity of the quartic calculation in local interaction models,is manageable computationally. The quartic (Bethe -Salpeter type) approximation is especially important in 1D and 2D models in which the symmetry broken state does not exists (the Mermin -Wagner theorem), although strong fluctuations dominate the physics at strong coupling. Unlike the lower order approximations, it respects the Mermin -Wagner theorem. The scheme is tested and exemplified on the single band 1D and 2D Hubbard model. *

show abstract

Section: Covariant Vs "Naive" Correlatormentioning

confidence: 99%

Covariant Bethe-Salpeter approximation in models of strongly correlated electron systems

Fan

Sun

et al. 2020

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…The present work is the first step in this direction. For concreteness, here we study the class of 1D Jastrow-Gutzwiller variational wave functions [26,46]. These states share two key features with their two-dimensional cousins employed as effective descriptions of quantum spin liquids: they describe extensive superpositions over some (spatially local) state basis, and they have in general as weights analytic functions of the space coordinates.…”

Section: Introductionmentioning

confidence: 99%

Parent Hamiltonian reconstruction of Jastrow-Gutzwiller wavefunctions

Turkeshi

Dalmonte

2020

SciPost Phys.

View full text Add to dashboard Cite

Variational wave functions have been a successful tool to investigate the properties of quantum spin liquids. Finding their parent Hamiltonians is of primary interest for the experimental simulation of these strongly correlated phases, and for gathering additional insights on their stability. In this work, we systematically reconstruct approximate spin-chain parent Hamiltonians for Jastrow-Gutzwiller wave functions, which share several features with quantum spin liquid wave-functions in two dimensions. Firstly, we determine the different phases encoded in the parameter space through their correlation functions and entanglement content. Secondly, we apply a recently proposed entanglement-guided method to reconstruct parent Hamiltonians to these states, which constrains the search to operators describing relativistic low-energy field theories -as expected for deconfined phases of gauge theories relevant to quantum spin liquids. The quality of the results is discussed using different quantities and comparing to exactly known parent Hamiltonians at specific points in parameter space. Our findings provide guiding principles for experimental Hamiltonian engineering of this class of states.

show abstract

“…A common form of Langevin dynamics is the so-called second-order LD (SOLD) [15,17,19,[26][27][28], in which the Newton equation of motion includes a friction term and a noisy force obeying the fluctuation-dissipation relation. An alternative is the first-order Langevin dynamics (FOLD) [15,29,30], which is conceptually simpler than SOLD because it does not have inertia and therefore only nuclear configurations are Boltzmann-sampled. FOLD is amenable to the introduction of a preconditioning matrix, which, by proper choice, dramatically increases the configurational sampling efficiency without affecting the accuracy [29].…”

mentioning

confidence: 99%

“…For any choice of the preconditioning matrix S, the generated trajectory of M samples the Boltzmann distribution at temperature T in the ∆ t → 0 and M → ∞ limits [30]. For finite values of M and ∆ t , the configurations can then be used to produce estimates of the thermal average of quantities A:…”

mentioning

confidence: 99%

See 1 more Smart Citation

Efficient Langevin dynamics for “noisy” forces

Arnon

Rabani

Neuhauser

et al. 2020

The Journal of Chemical Physics

View full text Add to dashboard Cite

Efficient Boltzmann-sampling using first-principles methods is challenging for extended systems due to the steep scaling of electronic structure methods with the system size. Stochastic approaches provide a gentler system-size dependency at the cost of introducing "noisy" forces, which serve to limit the efficiency of the sampling. In the first-order Langevin dynamics (FOLD), efficient sampling is achievable by combining a well-chosen preconditioning matrix S with a time-step-bias-mitigating propagator (Mazzola et al., Phys. Rev. Lett., 118, 015703 (2017)). However, when forces are noisy, S is set equal to the force-covariance matrix, a procedure which severely limits the efficiency and the stability of the sampling. Here, we develop a new, general, optimal, and stable sampling approach for FOLD under noisy forces. We apply it for silicon nanocrystals treated with stochastic density functional theory and show efficiency improvements by an order-of-magnitude.

show abstract

Quantum Monte Carlo Approaches for Correlated Systems

Cited by 318 publications

References 126 publications

Covariant Bethe-Salpeter approximation in models of strongly correlated electron systems

Covariant Bethe-Salpeter approximation in models of strongly correlated electron systems

Parent Hamiltonian reconstruction of Jastrow-Gutzwiller wavefunctions

Efficient Langevin dynamics for “noisy” forces

Contact Info

Product

Resources

About