arXiv subjects

Ian Pilé

Publications and source records attributed to Ian Pilé.

5 recordsLinked to original sources

arXiv2026

Algorithmic overlaps in the Baxter-Wu model: cluster dynamics under Novotny-Evertz updates

We study the spatial overlap of successive spin configurations generated by Markov chain Monte Carlo simulations of the Baxter-Wu model. Using the Novotny-Evertz sublattice-freezing single-cluster update, we track the mean and variance of the algorithmic overlap across the critical region. We show that, even in this three-spin model, the overlap acts as an algorithmic observable that follows the thermodynamics of the transition: the single-cluster overlap mean behaves like an order parameter, dropping from a finite ordered-phase plateau toward zero across $T_c$. The overlap does not diverge at criticality, instead it remains finite and its finite-size value decays as a clean power law, $U_2(T_c)\sim L^{-ψ}$, over eleven sizes with an exponent $ψ{=}0.378(4)$ smaller than the value $\approx0.42$ found for the Ising and Potts models under standard Fortuin-Kasteleyn cluster dynamics, indicating that it reflects the Novotny-Evertz sublattice-freezing dynamics rather than any static property of the model.

cond-mat.stat-mech↗

arXiv2026

Algorithmic overlaps as thermodynamic variables: from local to cluster Monte Carlo dynamics in critical phenomena

We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Swendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for models in different universality classes: Ising model, Potts model with three components, and four-state Potts model. The overlap of two successive Wolff clusters reflects critical behavior and can be used as an order parameter for the algorithm's dynamics. In the case of the Swendsen-Wang algorithm, similar behavior is demonstrated by the variance of the overlap of two consecutive lattice configurations, which behaves like an order parameter. Nothing similar is observed for the Metropolis algorithm, where the dynamics in the critical region are determined by the spin-flip frequency, which is equivalent to the acceptance rate. Thus, the critical behavior of the Wolff cluster overlap and of the variance of the configuration overlap in the Swendsen-Wang algorithm are naturally related to the critical behavior of geometric objects -- Fortuin-Kasteleyn clusters. Interestingly, in all cases the geometric quantity -- the configuration overlap or its variance -- reflects the thermodynamics of the phase transition.

cond-mat.stat-mech↗

arXiv2025

Superconductivity and trimers on attractive-$U$ Hubbard ladders

We investigate the interplay between superconducting correlations and trimer formation in polarized two-component Fermi gases confined to multileg attractive-$U$ Hubbard ladders. Employing density matrix renormalization group (DMRG) simulations, we explore the effects of spin-dependent tunneling amplitudes on these systems. Specifically, we analyze how bound states of three fermions (trimers) impact Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting correlations at commensurate charge carrier densities, where $2n_{\uparrow} = n_{\downarrow}$. In one-dimensional (1D) systems, trimer formation is known to suppress FFLO correlations exponentially. Our results demonstrate that this suppression persists on ladder lattices of small width, effectively mirroring the 1D behavior. However, we find a striking departure from the 1D regime as the ladder width increases. On ladders with a width of four legs, the influence of trimers on superconducting correlations becomes negligible, suggesting that wider ladder systems provide a distinct environment where FFLO-like pairing remains robust even in the presence of trimer states. These findings underscore the dimensional crossover in Hubbard systems and shed light on the mechanisms governing superconductivity and bound-state formation in strongly correlated fermionic systems. Our work has implications for understanding unconventional superconductivity in strongly correlated systems.

cond-mat.stat-mech↗

arXiv2024

Two-dimensional polarized superfluids under the prism of the fermion sign problem

Understanding if attractive fermions in an unbalanced occupation of its flavors can give rise to a superfluid state in two dimensions (2D), realizing the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state, presents a long-standing question. A limitation on its solution by numerics is posed by the sign problem, which constrains the applicability of quantum Monte Carlo techniques at sufficiently low temperatures and large lattice sizes, where a potential signature of polarized superfluidity would be unambiguous. By using a recently explored argument that the sign problem may be used instead to infer quantum critical behavior, we explore the regime where partial polarization occurs in the phase diagram, further showing that the average sign $\langle {\cal S}\rangle$ of quantum Monte Carlo weights tracks the criticality between balanced (or fully polarized) and polarized phases. Using the attractive Hubbard model with an unbalanced population, our investigation expands the scope of problems in which $\langle {\cal S}\rangle$ can be used for monitoring critical behavior, providing compelling albeit indirect evidence for the robustness of an FFLO phase in 2D.

cond-mat.str-el↗

arXiv2023

Dimensional crossover on multileg attractive-$U$ Hubbard ladders

We study the ground state properties of a polarized two-component Fermi gas on multileg attractive-$U$ Hubbard ladders. Using exact diagonalization and density matrix renormalization group method simulations, we construct grand canonical phase diagrams for ladder widths of up to $W=5$ and varying perpendicular geometries, characterizing the quasi-one-dimensional regime of the dimensional crossover. We unveil a multicritical point marking the onset of partial polarization in those phase diagrams, a candidate regime of finite-momentum pairing. We compare our findings with recent experimental and theoretical studies of quasi-one-dimensional polarized Fermi gases.

cond-mat.quant-gas↗