Quantum critical points and the sign problem

Science, Journal Year: 2022, Volume and Issue: 375(6579), P. 418 - 424

Published: Jan. 27, 2022

The "sign problem" (SP) is the fundamental limitation to simulations of strongly correlated materials in condensed matter physics, solving quantum chromodynamics at finite baryon density, and computational studies nuclear matter. As a result, it part reason fields such as ultra-cold atomic physics are so exciting: they can provide emulators models that could not otherwise be solved, due SP. For same reason, also one primary motivations behind computation. It often argued SP intrinsic particular Hamiltonians, since details how onsets, its eventual occurrence, altered by choice algorithm or many-particle basis. Despite that, we show determinant Monte Carlo (DQMC) quantitatively linked critical behavior. We demonstrate this via number including spinful spinless Hubbard Hamiltonians on honeycomb lattice ionic Hamiltonian, all whose properties relatively well understood. then propose reinterpretation low average sign for model square when away from half-filling, an important open problem terms onset pseudogap behavior exotic superconductivity. Our study charts path exploiting QMC understand behavior, rather than solely obstacle prevents many-body temperature.

Language: Английский

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Thermodynamics and its prediction and CALPHAD modeling: Review, state of the art, and perspectives

Calphad, Journal Year: 2023, Volume and Issue: 82, P. 102580 - 102580

Published: June 26, 2023

Language: Английский

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Temperature Dependence of Spin and Charge Orders in the Doped Two-Dimensional Hubbard Model

Physical Review X, Journal Year: 2023, Volume and Issue: 13(1)

Published: Jan. 24, 2023

State-of-the-art numerical techniques suggest that charge order in the 2D Hubbard model sets at a nonzero temperature, answering major open question physics of this paradigmatic quantum materials.

Language: Английский

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Thermodynamic Characteristic for a Correlated Flat-Band System with a Quantum Anomalous Hall Ground State

Physical Review Letters, Journal Year: 2023, Volume and Issue: 130(1)

Published: Jan. 3, 2023

While the ground-state phase diagram of correlated flat-band systems has been intensively investigated, dynamic and thermodynamic properties such lattice models are less explored, but it is latter which most relevant to experimental probes (transport, quantum capacitance, spectroscopy) moiré materials as twisted bilayer graphene. Here we show, by means momentum-space Monte Carlo exact diagonalization, in chiral limit there exists a unique characteristic for model with interaction-driven anomalous Hall (QAH) ground state, namely, transition from QAH insulator metallic state takes place at much lower temperature compared zero-temperature single-particle gap generated long-range Coulomb interaction. Such low comes proliferation excitonic particle-hole excitations, transfers electrons across between different topological bands restore broken time-reversal symmetry gives rise pronounced enhancement charge compressibility. Future experiments, verify generic characteristics, proposed.

Language: Английский

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Integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulations

Physical review. B./Physical review. B, Journal Year: 2024, Volume and Issue: 109(20)

Published: May 21, 2024

Exponential observables, formulated as $ln\ensuremath{\langle}{e}^{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}}\ensuremath{\rangle}$ where $\stackrel{\ifmmode \^{}\fi{}}{X}$ is an extensive quantity, play a critical role in the study of quantum many-body systems, examples which include free energy and entanglement entropy. Given that ${e}^{X}$ becomes exponentially large (or small) thermodynamic limit, accurate computation expectation value this exponential quantity presents significant challenge. In paper, we propose comprehensive algorithm to quantify these observables interacting fermion utilizing determinant Monte Carlo method. We have applied two-dimensional square-lattice half-filled Hubbard model $\ensuremath{\pi}$-flux t-V model. case at strong-coupling our method showcases accuracy improvement on compared conventional methods are derived from internal energy, model, indicate offers precise determination second-order phase transition. also illustrate approach delivers highly efficient measurements $n\mathrm{th}$ R\'enyi Even more noteworthy comes without incurring increases computational complexity. This effectively suppresses fluctuations can be easily generalized other models.

Language: Английский

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Boosting determinant quantum Monte Carlo with submatrix updates: Unveiling the phase diagram of the 3D Hubbard model

SciPost Physics, Journal Year: 2025, Volume and Issue: 18(2)

Published: Feb. 17, 2025

Determinant Quantum Monte Carlo (DQMC) provides numerically exact solutions for strongly correlated fermionic systems but faces significant computational challenges with increasing system size. While submatrix updates were originally developed Hirsch-Fye QMC onsite interactions at finite temperatures, their comprehensive application in DQMC has remained unexplored despite noted algorithmic similarities. We present the first of DQMC, significantly extending beyond original scope by enabling simulations extended and zero temperature. Building upon conventional fast delay updates, our generalized implementation achieves an order-of-magnitude improvement efficiency, half-filled Hubbard model on lattices up to 8,000 sites - a scale previously challenging standard implementations. This enhanced capability allows us accurately determine finite-temperature phase diagram 3D half-filling. Our findings not only shed light transitions within these complex also pave way more effective electrons, potentially guiding experimental efforts cold atom model.

Language: Английский

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Topological origin of flat bands as pseudo-Landau levels in uniaxial strained graphene nanoribbons and induced magnetic ordering due to electron-electron interactions

Physical review. B./Physical review. B, Journal Year: 2023, Volume and Issue: 107(23)

Published: June 23, 2023

Flat-bands play a central role in the presence of correlated phases Moir\'e and other modulated two dimensional systems. In this work, flat-bands are shown to exist uniaxially periodic strained graphene. Such strain should be produced for example by substrate. The model is thus mapped into one-dimensional effective Hamiltonian allows find conditions having flat-bands, i.e., long-wavelength modulation only on each one bipartite graphene sublattices, while tagged field between neighboring carbon atoms. origin such tracked down existence topological localized wavefunctions at domain walls separating different regions, with non-uniform Su-Schriffer-Hegger (SSH) type coupling. Thereafter, system continuum allowing explain numerical results terms Jackiw-Rebbi pseudo-Landau levels. Finally, interplay obtained electron-electron interaction explored through Hubbard model. within mean-field approximation indicate that induce N\'eel antiferromagnetic ferromagnetic domains even very weak interaction. present provides simple platform understand physical levels effects

Language: Английский

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Existence of real time quantum path integrals

Annals of Physics, Journal Year: 2023, Volume and Issue: 454, P. 169315 - 169315

Published: April 20, 2023

Many interesting physical theories have analytic classical actions. We show how Feynman's path integral may be defined non-perturbatively, for such theories, without a Wick rotation to imaginary time. start by introducing class of smooth regulators which render interference integrals absolutely convergent and thus unambiguous. The analyticity the allows us use Cauchy's theorem deform integration domain onto set relevant, complex "thimbles" (or generalized steepest descent contours) each associated with saddle. regulator can then removed obtain an exact, non-perturbative representation. why usual method gradient flow, used identify relevant saddles finite-dimensional oscillatory integrals, fails in infinite-dimensional case. For troublesome high frequency modes, we replace it call "eigenflow" employ infinite-dimensional, "eigenthimble" over real time is convergent. bound modes corresponding Wiener measure free particle. Using dominated convergence infer that interacting defines good measure. While more intricate than its Euclidean counterpart, superior several respects. It seems particularly well-suited as quantum gravity where theory well developed but does not exist.

Language: Английский

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Universality and critical exponents of the fermion sign problem

Physical review. B./Physical review. B, Journal Year: 2023, Volume and Issue: 107(24)

Published: June 29, 2023

Initial characterizations of the fermion sign problem focused on its evolution with spatial lattice size $L$ and inverse temperature $\ensuremath{\beta}$, emphasizing implications exponential nature decay average $\ensuremath{\langle}\mathcal{S}\ensuremath{\rangle}$ for complexity solution associated limitations quantum Monte Carlo studies strongly correlated materials. Early interest was also density $\ensuremath{\rho}$, either because commensurate filling is often special symmetries which absent, or particular fillings are primary targets, e.g., those densities, maximize superconducting transition (the top ``dome'' cuprate systems). Here we describe an analysis problem, demonstrates that spin-resolved $\ensuremath{\langle}{\mathcal{S}}_{\ensuremath{\sigma}}\ensuremath{\rangle}$ already possesses signatures universal behavior traditionally order parameters, even in absence symmetry protection makes $\ensuremath{\langle}\mathcal{S}\ensuremath{\rangle}=1$. When appropriately scaled, exhibits crossings data collapse. Moreover, show these behaviors occur vicinity critical points three well-understood models, exhibiting second-order Kosterlitz-Thouless phase transitions. Our results pave way using as a minimal correlator can potentially criticality variety fermionic many-body problems.

Language: Английский

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SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions

SciPost Physics Codebases, Journal Year: 2024, Volume and Issue: unknown

Published: May 28, 2024

We introduce the SmoQyDQMC.jl package, a Julia implementation of determinant quantum Monte Carlo algorithm. supports generalized tight-binding Hamiltonians with on-site Hubbard and electron-phonon ( e e -ph) interactions, including non-linear -ph coupling anharmonic lattice potentials. Our uses hybrid methods exact forces for sampling phonon fields, enabling efficient simulation low-energy branches, acoustic phonons. The package also flexible scripting interface, allowing users to adapt it different workflows interface other software packages in ecosystem. code this can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDQMC.jl or installed using manager. online documentation, examples, obtained document page https://smoqysuite.github.io/SmoQyDQMC.jl/stable/.

Language: Английский

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