arXiv subjects

Sebastiano Peotta

Publications and source records attributed to Sebastiano Peotta.

At least 19 recordsLinked to original sources

arXiv2026

Parity-dependent double degeneracy and spectral statistics in the projected dice lattice

We investigate the spectral statistics of an interacting fermionic system derived by projecting the Hubbard interaction onto the two lowest-energy, degenerate flat bands of the dice lattice subjected to a $\pi$-flux. Surprisingly, the distributions of level spacings and gap ratios correspond to distinct Gaussian ensembles, depending on the parity of the particle number. For an even number of particles, the spectra conform to the Gaussian Orthogonal Ensemble, as expected for a time-reversal-symmetric Hamiltonian. In stark contrast, the odd-parity sector exhibits exact double degeneracy of all eigenstates even after resolving all known symmetries, and the Gaussian Unitary Ensemble accurately describes the spacing distribution between these doublets. The simultaneous emergence of two different random-matrix ensembles within a single physical system constitutes an unprecedented finding, opening new avenues for both random matrix theory and flat-band physics.

cond-mat.str-el↗

arXiv2025

Supersolid phase in two-dimensional soft-core bosons at finite temperature

The supersolid phase of soft-core bosons in two dimensions is investigated using the self-consistent Hartree-Fock and quantum Monte Carlo methods. An approximate phase diagram at finite temperatures is initially constructed using the mean-field approach, which is subsequently validated through precise path-integral simulations, enabling a microscopic characterization of the various phases. Superfluid and melting/freezing transitions are analyzed through the superfluid density and the long-range behavior of correlation functions associated with positional and orientational order, in accordance with the general picture of Berezinskii-Kosterlitz-Thouless transitions. A broad region at low temperatures is identified where the supersolid phase exists, separating the uniform superfluid phase from the normal quasi-crystal phase. Additionally, a potential intermediate hexatic phase with quasi long-range orientational order is identified in a narrow region between the normal solid and fluid phases. These findings establish self-consistent Hartree-Fock theory beyond the local density approximation as an effective tool, complementary to computationally intensive quantum Monte Carlo simulations, for investigating the melting of the supersolid phase and the possible emergence of the hexatic superfluid phase in bosonic systems with various interaction potentials.

cond-mat.quant-gas↗

arXiv2024

Coexistence of ergodic and non-ergodic behavior and level spacing statistics in a one-dimensional model of a flat band superconductor

Motivated by recent studies of the projected dice lattice Hamiltonian [K. Swaminathan et al., Phys. Rev. Research 5, 043215 (2023)], we introduce the on-site/bond singlet (OBS) model, a one-dimensional model of a flat band superconductor, in order to better understand the quasiparticle localization and interesting coexistence of ergodic and non-ergodic behavior present in the former model. The OBS model is the sum of terms that have direct counterparts in the projected dice lattice Hamiltonian, each of which is parameterized by a coupling constant. Exact diagonalization reveals that the energy spectrum and non-equilibrium dynamics of the OBS model are essentially the same as that of the dice lattice for some values of the coupling constants. The quasiparticle localization and breaking of ergodicity manifest in a striking manner in the level spacing distribution. Its near Poissonian form provides evidence for the existence of local integrals of motion and establishes the OBS model as a non-trivial integrable generalization of the projected Creutz ladder Hamiltonian. These results show that level spacing statistics is a promising tool to study quasiparticle excitations in flat band superconductors.

cond-mat.supr-con↗

arXiv2024

Superfluid weight in the isolated band limit within the generalized random phase approximation

The superfluid weight of a generic lattice model with attractive Hubbard interaction is computed analytically in the isolated band limit within the generalized random phase approximation. Time-reversal symmetry, spin rotational symmetry, and the uniform pairing condition are assumed. It is found that the relation obtained in [https://link.aps.org/doi/10.1103/PhysRevB.106.014518] between the superfluid weight in the flat band limit and the so-called minimal quantum metric is valid even at the level of the generalized random phase approximation. For an isolated, but not necessarily flat, band it is found that the correction to the superfluid weight obtained from the generalized random phase approximation $D_{\rm s}^{(1)} = D_{\rm s,c}^{(1)}+D_{\rm s,g}^{(1)}$ is also the sum of a conventional contribution $D_{\rm s,c}^{(1)}$ and a geometric contribution $D_{\rm s,g}^{(1)}$, as in the case of the known mean-field result $D_{\rm s}^{(0)}=D_{\rm s,c}^{(0)}+D_{\rm s,g}^{(0)}$, in which the geometric term $D_{\rm s,g}^{(0)}$ is a weighted average of the quantum metric. The conventional contribution is geometry independent, that is independent of the orbital positions, while it is possible to find a preferred, or natural, set of orbital positions such that $D_{\rm s,g}^{(1)}=0$. Useful analytic expressions are derived for both the natural orbital positions and the minimal quantum metric, including its extension to bands that are not necessarily flat. Finally, using some simple examples, it is argued that the natural orbital positions may lead to a more refined classification of the topological properties of the band structure.

cond-mat.supr-con↗

arXiv2023

Signatures of many-body localization of quasiparticles in a flat band superconductor

We construct a class of exact eigenstates of the Hamiltonian obtained by projecting the Hubbard interaction term onto the flat band subspace of a generic lattice model. These exact eigenstates are many body states in which an arbitrary number of localized fermionic particles coexist with a sea of mobile Cooper pairs with zero momentum. By considering the dice lattice as an example, we provide evidence that these exact eigenstates are in fact manifestation of local integrals of motions of the projected Hamiltonian. In particular the spin and particle densities retain memory of the initial state for a very long time, if localized unpaired particles are present at the beginning of the time evolution. This shows that many-body localization of quasiparticles and superfluidity can coexist even in generic two-dimensional lattice models with flat bands, for which it is not known how to construct local conserved quantities. Our results open new perspectives on the old condensed matter problem of the interplay between superconductivity and localization.

cond-mat.supr-con↗

arXiv2023

Quantum geometry in superfluidity and superconductivity

We review the theoretical description of the role of quantum geometry in superfluidity and superconductivity of multiband systems, with focus on flat bands where quantum geometry is wholly responsible for supercurrents. This review differs from previous ones in that it is based on the most recent understanding of the theory: the dependence of the self-consistent order parameter on the supercurrent is properly taken into account, and the superfluid weight in a flat band becomes proportional to the minimal quantum metric. We provide a recap of basic quantum geometric quantities and the concept of superfluid density. The geometric contribution of superconductivity is introduced via considering the two-body problem. The superfluid weight of a multiband system is derived within mean-field theory, leading to a topological bound of flat band superconductivity. The physical interpretation of the flat band supercurrent in terms of Wannier function overlaps is discussed.

cond-mat.quant-gas↗

arXiv2022

Superconductivity, generalized random phase approximation and linear scaling methods

The superfluid weight is an important observable of superconducting materials since it is related to the London penetration depth of the Meissner effect. It can be computed from the change in the grand potential (or free energy) in response to twisted boundary conditions in a torus geometry. Here we review the Bardeen-Cooper-Schrieffer mean-field theory emphasizing its origin as a variational approximation for the grand potential. The variational parameters are the effective fields that enter in the mean-field Hamiltonian, namely the Hartree-Fock potential and the pairing potential. The superfluid weight is usually computed by ignoring the dependence of the effective fields on the twisted boundary conditions. However, it has been pointed out in recent works that this can lead to unphysical results, particularly in the case of lattice models with flat bands. As a first result, we show that taking into account the dependence of the effective fields on the twisted boundary conditions leads in fact to the generalized random phase approximation. Our second result is providing the mean-field grand potential as an explicit function of the one-particle density matrix. This allows us to derive the expression for the superfluid weight within the generalized random phase approximation in a transparent manner. Moreover, reformulating mean-field theory as a well-posed minimization problem in terms of the one-particle density matrix is a first step towards the application to superconducting systems of the linear scaling methods developed in the context of electronic structure theory.

cond-mat.supr-con↗

arXiv2022

Suppression of non-equilibrium quasiparticle transport in flat band superconductors

We study non-equilibrium transport through a superconducting flat-band lattice in a two-terminal setup with the Schwinger-Keldysh method. We find that quasiparticle transport is suppressed and coherent pair transport dominates. For superconducting leads, the AC supercurrent overcomes the DC current which relies on multiple Andreev reflections. With normal-normal and normal-superconducting leads, the Andreev reflection and normal currents vanish. Flat band superconductivity is thus promising not only for high critical temperatures but also for suppressing unwanted quasiparticle processes.

cond-mat.supr-con↗

arXiv2022

Dynamical quantum phase transitions in strongly correlated two-dimensional spin lattices following a quench

Dynamical quantum phase transitions are at the forefront of current efforts to understand quantum matter out of equilibrium. Except for a few exactly solvable models, predictions of these critical phenomena typically rely on advanced numerical methods. However, those approaches are mostly restricted to one dimension, making investigations of two-dimensional systems highly challenging. Here, we present evidence of dynamical quantum phase transitions in strongly correlated spin lattices in two dimensions. To this end, we apply our recently developed cumulant method [Phys. Rev. X 11, 041018 (2021)] to determine the zeros of the Loschmidt amplitude in the complex plane of time and predict the crossing points of the thermodynamic lines of zeros with the real-time axis, where dynamical quantum phase transitions occur. We find the critical times of a two-dimensional quantum Ising lattice and the XYZ model with ferromagnetic or antiferromagnetic couplings. We also show how dynamical quantum phase transitions can be predicted by measuring the initial energy fluctuations, for example, in quantum simulators or other engineered quantum systems.

cond-mat.str-el↗

arXiv2022

Universal suppression of superfluid weight by disorder independent of quantum geometry and band dispersion

Motivated by the experimental progress in controlling the properties of the energy bands in superconductors, significant theoretical efforts have been devoted to study the effect of the quantum geometry and the flatness of the dispersion on the superfluid weight. In conventional superconductors, where the energy bands are wide and the Fermi energy is large, the contribution due to the quantum geometry is negligible, but in the opposite limit of flat-band superconductors the superfluid weight originates purely from the quantum geometry of Bloch wave functions. Here, we study how the energy band dispersion and the quantum geometry affect the disorder-induced suppression of the superfluid weight. Surprisingly, we find that the disorder-dependence of the superfluid weight is universal across a variety of models, and independent of the quantum geometry and the flatness of the dispersion. Our results suggest that a flat-band superconductor is as resilient to disorder as a conventional superconductor.

cond-mat.supr-con↗

arXiv2021

Determination of dynamical quantum phase transitions in strongly correlated many-body systems using Loschmidt cumulants

Dynamical phase transitions extend the notion of criticality to non-stationary settings and are characterized by sudden changes in the macroscopic properties of time-evolving quantum systems. Investigations of dynamical phase transitions combine aspects of symmetry, topology, and non-equilibrium physics, however, progress has been hindered by the notorious difficulties of predicting the time evolution of large, interacting quantum systems. Here, we tackle this outstanding problem by determining the critical times of interacting many-body systems after a quench using Loschmidt cumulants. Specifically, we investigate dynamical topological phase transitions in the interacting Kitaev chain and in the spin-1 Heisenberg chain. To this end, we map out the thermodynamic lines of complex times, where the Loschmidt amplitude vanishes, and identify the intersections with the imaginary axis, which yield the real critical times after a quench. For the Kitaev chain, we can accurately predict how the critical behavior is affected by strong interactions, which gradually shift the time at which a dynamical phase transition occurs. We also discuss the experimental perspectives of predicting the first critical time of a quantum many-body system by measuring the energy fluctuations in the initial state, and we describe the prospects of implementing our method on a near-term quantum computer with a limited number of qubits. Our work demonstrates that Loschmidt cumulants are a powerful tool to unravel the far-from-equilibrium dynamics of strongly correlated many-body systems, and our approach can immediately be applied in higher dimensions.

cond-mat.str-el↗

arXiv2021

Flat band transport and Josephson effect through a finite-size sawtooth lattice

We study theoretically the transport through a finite-size sawtooth lattice coupled to two fermionic reservoirs kept in the superfluid state. We focus on the DC Josephson effect and find that the flat band states of the sawtooth lattice can support larger critical current and at higher temperature than the dispersive band states. However, for this to occur the boundary states of the finite-size lattice need to be tuned at resonance with the bulk flat band states by means of additional boundary potentials. We show that transport in a two-terminal configuration can reveal the salient features of the geometric contribution of flat band superconductivity, namely the linear dependence of key quantities, such as the critical current and critical temperature, on the interaction. Our results are based on parameters of a realistic experimental lattice potential, and we discuss the conditions one needs to reach to observe the predicted effects experimentally.

cond-mat.quant-gas↗

arXiv2020

Flat band induced non-Fermi liquid behavior of multicomponent fermions

We investigate multicomponent fermions in a flat band and predict experimental signatures of non-Fermi liquid behavior. We use dynamical mean-field theory to obtain the density, double occupancy and entropy in a Lieb lattice for $\mathcal{N} = 2$ and $\mathcal{N} = 4$ components. We derive a mean-field scaling relation between the results for different values of $\mathcal{N}$, and study its breakdown due to beyond-mean field effects. The predicted signatures occur at temperatures above the Néel temperature and persist in presence of a harmonic trapping potential, thus they are observable with current ultracold gas experiments.

cond-mat.quant-gas↗

arXiv2019

Preformed pairs in flat Bloch bands

In a flat Bloch band the kinetic energy is quenched and single particles cannot propagate since they are localized due to destructive interference. Whether this remains true in the presence of interactions is a challenging question because a flat dispersion usually leads to highly correlated ground states. Here we compute numerically the ground state energy of lattice models with completely flat band structure in a ring geometry. We find that the energy as a function of the magnetic flux threading the ring has a half-flux quantum $Φ_0/2 = hc/(2e)$ period, indicating that only bound pairs of particles with charge $2e$ are propagating, while single quasiparticles with charge $e$ remain localized. We show analytically in one dimension that in fact the whole many-body spectrum has the same periodicity. Our analytical arguments are valid for both bosons and fermions, for generic interactions respecting some symmetries of the lattice and at arbitrary temperatures. Moreover we construct an extensive number of exact conserved quantities for the one dimensional lattice models. These conserved quantities are associated to the occupation of localized single quasiparticle states. Our results imply that in lattice models with flat bands preformed pairs dominate transport even above the critical temperature of the transition to a superfluid state.

cond-mat.str-el↗

arXiv2018

Quantum metric and effective mass of a two-body bound state in a flat band

We consider two-body bound states in a flat band of a multiband system. The existence of pair dispersion predicts the possibility of breaking the degeneracy of the band and creating order, such as superconductivity. Within a separable interaction potential approximation, we find that finiteness of the effective mass of a bound pair is determined by a band structure invariant, which in the uniform case becomes the quantum metric. The results offer a simple foundation to understand and predict flat band superconductivity. We propose an experiment to test the interaction-induced pair motion.

cond-mat.supr-con↗

arXiv2018

Spin-Imbalanced Pairing and Fermi Surface Deformation in Flat Bands

We study the attractive Hubbard model with spin imbalance on two lattices featuring a flat band: the Lieb and kagome lattices. We present mean-field phase diagrams featuring exotic superfluid phases, similar to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, whose stability is confirmed by dynamical mean-field theory (DMFT). The nature of the pairing is found to be richer than just the Fermi surface shift responsible for the usual FFLO state. The presence of a flat band allows for changes in the particle momentum distributions at null energy cost. This facilitates formation of nontrivial superfluid phases via multiband Cooper pair formation: the momentum distribution of the spin component in the flat band deforms to mimic the Fermi surface of the other spin component residing in a dispersive band. The Fermi surface of the unpaired particles that are typical for gapless superfluids becomes deformed as well. The results highlight the profound effect of flat dispersions on Fermi surface instabilities, and provide a potential route for observing spin-imbalanced superfluidity and superconductivity.

cond-mat.quant-gas↗

arXiv2017

Wave packet dynamics of Bogoliubov quasiparticles: quantum metric effects

We study the dynamics of the Bogoliubov wave packet in superconductors and calculate the supercurrent carried by the wave packet. We discover an anomalous contribution to the supercurrent, related to the quantum metric of the Bloch wave function. This anomalous contribution is most important for flat or quasiflat bands, as exemplified by the attractive Hubbard models on the Creutz ladder and sawtooth lattice. Our theoretical framework is general and can be used to study a wide variety of phenomena, such as spin transport and exciton transport.

cond-mat.supr-con↗

arXiv2017

Phase-dependent noise in Josephson junctions

In addition to the usual superconducting current, Josephson junctions (JJs) support a phase-dependent conductance related to the retardation effect of tunneling quasi-particles. This introduces a dissipative current with a memory-resistive (memristive) character and thus should also affect the current noise. By means of the microscopic theory of tunnel junctions we compute the complete current autocorrelation function of a Josephson tunnel junction and show that this memristive component gives rise to a non-stationary, phase-dependent noise. As a consequence, dynamic and thermal noise necessarily show a phase dependence otherwise absent in nondissipative JJ models. This phase dependence may be realized experimentally as a hysteresis effect if the unavoidable time averaging of the experimental probe is shorter than the period of the Josephson phase.

cond-mat.mes-hall↗