Fermion Model Research Articles

Effective field theories for dark matter pairs in the early universe: center-of-mass recoil effects

For non-relativistic thermal dark matter, close-to-threshold effects largely dominate the evolution of the number density for most of the times after thermal freeze-out, and hence affect the cosmological relic density. A precise evaluation of the relevant interaction rates in a thermal medium representing the early universe includes accounting for the relative motion of the dark matter particles and the thermal medium. We consider a model of dark fermions interacting with a plasma of dark gauge bosons, which is equivalent to thermal QED. The temperature is taken to be smaller than the dark fermion mass and the inverse of the typical size of the dark fermion-antifermion bound states, which allows for the use of non-relativistic effective field theories. For the annihilation cross section, bound-state formation cross section, bound-state dissociation width and bound-state transition width of dark matter fermion-antifermion pairs, we compute the leading recoil effects in the reference frame of both the plasma and the center-of-mass of the fermion-antifermion pair. We explicitly verify the Lorentz transformations among these quantities. We evaluate the impact of the recoil corrections on the dark matter energy density. Our results can be directly applied to account for the relative motion of quarkonia in the quark-gluon plasma formed in heavy-ion collisions. They may be also used to precisely assess thermal effects in atomic clocks based on atomic transitions; the present work provides a first field theory derivation of time dilation for these processes in vacuum and in a medium.

Microscopic Origin of the Quantum Mpemba Effect in Integrable Systems.

The highly complicated nature of far from equilibrium systems can lead to a complete breakdown of the physical intuition developed in equilibrium. A famous example of this is the Mpemba effect, which states that nonequilibrium states may relax faster when they are further from equilibrium or, put another way, hot water can freeze faster than warm water. Despite possessing a storied history, the precise criteria and mechanisms underpinning this phenomenon are still not known. Here, we study a quantum version of the Mpemba effect that takes place in closed many-body systems with a U(1) conserved charge: in certain cases a more asymmetric initial configuration relaxes and restores the symmetry faster than a more symmetric one. In contrast to the classical case, we establish the criteria for this to occur in arbitrary integrable quantum systems using the recently introduced entanglement asymmetry. We describe the quantum Mpemba effect in such systems and relate the properties of the initial state, specifically its charge fluctuations, to the criteria for its occurrence. These criteria are expounded using exact analytic and numerical techniques in several examples, a free fermion model, the Rule 54 cellular automaton, and the Lieb-Liniger model.

Nonlocal fermions with local interactions and the SYK model

One of the most promising routes to non-fermi liquids and strange metals has been through SYK models (Sachdev 2010 Phys. Rev. Lett. 105 151602) which necessarily involve large flavor degrees of freedom and interactions with imposed disorder. We introduce an interacting model of nonlocal spinless fermions in which large flavor and effective disorder emerge spontaneously in the extreme nonlocal limit. This model may be thought of as an expansion in a dimensionless ‘locality scale,’ α, with the limit α→0 recovering a conventional local action. For finite α, the resulting interacting nonlocal action exhibits a large number of low-energy degrees of freedom—proportional to α—and the structure factor mediating the local interactions between these fermions is effectively random for large α. In one dimension, with finite α, we show that interactions are marginal to the one loop level (as they are in the conventional local case), preserving a gapless phase. At large α the interaction strength becomes comparable to the bandwidth and we analyze this large flavor limit in a manner similar to the diagrammatic approach to SYK. As α is increased we argue that the gapless phase established by conventional RG possibly crosses over to a gapless SYK phase, although the ‘melon’ diagrams are not exclusively dominant. We speculate on how this model might arise physically from an S-matrix connecting pure excited states—rather than the vacuum—to access finite temperature interacting fermions.

Topological heavy fermions in magnetic field

The recently introduced topological heavy fermion model (THFM) provides a means for interpreting the low-energy electronic degrees of freedom of the magic angle twisted bilayer graphene as hybridization amidst highly dispersing topological conduction and weakly dispersing localized heavy fermions. In order to understand the Landau quantization of the ensuing electronic spectrum, a generalization of THFM to include the magnetic field B is desired, but currently missing. Here we provide a systematic derivation of the THFM in B and solve the resulting model to obtain the interacting Hofstadter spectra for single particle charged excitations. While naive minimal substitution within THFM fails to correctly account for the total number of magnetic subbands within the narrow band i.e., its total Chern number, our method—based on projecting the light and heavy fermions onto the irreducible representations of the magnetic translation group— reproduces the correct total Chern number. Analytical results presented here offer an intuitive understanding of the nature of the (strongly interacting) Hofstadter bands.

Electron-electron attraction via Coulomb correlations and possible superconductivity in a 1D electron liquid on a rigid neutralizing background

Conditions at which a quasi-one-dimensional (1D) electron system can be considered as a quantum liquid of impenetrable charged particles are theoretically analyzed. In the presence of an inert, neutralizing background, a motion of impenetrable electrons is shown to expose a positive charge, resulting in an effective mutual attraction of infinite range. As a result, all electrons are involved in the long-range pairing. A model of spinless fermions with infinitesimal attraction of infinite range is proposed to describe the excitation spectrum and the superconducting gap in low-density 1D electron channels. In contrast with the conventional theory, the energy gap does not contain exponentially small factors. It depends mostly on the Coulombic parameters of the system, which guides practical aspects of high-temperature superconductivity.

The Dynamics of the Hubbard Model Through Stochastic Calculus and Girsanov Transformation

As a typical quantum many body problem, we consider the time evolution of density matrix elements in the Bose-Hubbard model. For an arbitrary initial state, these quantities can be obtained from an SDE or stochastic differential equation system. To this SDE system, a Girsanov transformation can be applied. This has the effect that all the information from the initial state moves into the drift part, into the mean field part, of the transformed system. In the large N limit with g=UN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g=UN$$\\end{document} fixed, the diffusive part of the transformed system vanishes and as a result, the exact quantum dynamics is given by an ODE system which turns out to be the time dependent discrete Gross Pitaevskii equation. For the two site Bose-Hubbard model, the GP equation reduces to the mathematical pendulum and the difference of expected number of particles at the two lattice sites is equal to the velocity of that pendulum which is either oscillatory or it can have rollovers which then corresponds to the self trapping or insulating phase. As a by-product, we also find an equivalence of the mathematical pendulum with a quartic double well potential. Collapse and revivals are a more subtle phenomenom, in order to see these the diffusive part of the SDE system or quantum corrections have to be taken into account. This can be done with an approximation and collapse and revivals can be reproduced, numerically and also through an analytic calculation. Since expectation values of Fresnel or Wiener diffusion processes, we write the density matrix elements exactly in this way, can be obtained from parabolic second order PDEs, we also obtain various exact PDE representations. The paper has been written with the goal to come up with an efficient calculation scheme for quantum many body systems and as such the formalism is generic and applies to arbitrary dimension, arbitrary hopping matrices and, with suitable adjustments, to fermionic models.

Physical and unphysical regimes of self-consistent many-body perturbation theory

In the standard framework of self-consistent many-body perturbation theory, the skeleton series for the self-energy is truncated at a finite order N and plugged into the Dyson equation, which is then solved for the propagator G_NGN. We consider two examples of fermionic models, the Hubbard atom at half filling and its zero space-time dimensional simplified version. First, we show that G_NGN converges when N\to∞N→∞ to a limit G_∞\,G∞, which coincides with the exact physical propagator G_{exact}Gexact at small enough coupling, while G_∞ ≠ G_{exact}G∞≠Gexact at strong coupling. This follows from the findings of [Phys. Rev. Lett. 114, 156402 (2015)] and an additional subtle mathematical mechanism elucidated here. Second, we demonstrate that it is possible to discriminate between the G_∞=G_{exact}G∞=Gexact and G_∞≠G_{exact}G∞≠Gexact regimes thanks to a criterion which does not require the knowledge of G_{exact}Gexact, as proposed in [Phys. Rev. B 93, 161102 (2016)].

Dynamical quantum phase transitions following a noisy quench

We study how time-dependent energy fluctuations impact the dynamical quantum phase transitions (DQPTs) following a noisy ramped quench of the transverse magnetic field in a quantum Ising chain. By numerically solving the stochastic Schrödinger equation of the mode-decoupled fermionic Hamiltonian of the problem, we identify two generic scenarios: Depending on the amplitude of the noise and the rate of the ramp, the expected periodic sequence of noiseless DQPTs may either be uniformly shifted in time or else replaced by a disarray of closely spaced DQPTs. Guided by an exact noise master equation, we trace the phenomenon to the interplay between noise-induced excitations which accumulate during the quench and the near-adiabatic dynamics of the massive modes of the system. Our analysis generalizes to any one-dimensional fermionic two-band model subject to a noisy quench. Published by the American Physical Society 2024

Sketching phase diagrams using low-depth variational quantum algorithms

Mapping out phase diagrams of quantum systems using classical simulations can be challenging or intractable due to the computational resources required to simulate even small quantum systems far away from the thermodynamic limit. We investigate using quantum computers and the variational quantum eigensolver (VQE) for this task. In contrast to the task of preparing the exact ground state using VQE, sketching phase diagrams might require less quantum resources and accuracy, because low fidelity approximations to the ground state may be enough to correctly identify different phases. We used classical numerical simulations of low-depth VQE circuits to compute order parameters for four well-studied spin and fermion models which represent a mix of 1D and 2D, and exactly-solvable and classically hard systems. We find that it is possible to predict the location of phase transitions up to reasonable accuracy using states produced by VQE even when their overlap with the true ground state is small. Further, we introduce a model-agnostic predictor of phase transitions based on the speed with which the VQE energy improves with respect to the circuit depth, and find that in some cases this is also able to predict phase transitions.

Exact Results for a Boundary-Driven Double Spin Chain and Resource-Efficient Remote Entanglement Stabilization

We derive an exact solution for the steady state of a setup where two XX-coupled N-qubit spin chains (with possibly nonuniform couplings) are subject to boundary Rabi drives and common boundary loss generated by a waveguide (either bidirectional or unidirectional). For a wide range of parameters, this system has a pure entangled steady state, providing a means for stabilizing remote multiqubit entanglement without the use of squeezed light. Our solution also provides insights into a single boundary-driven dissipative XX spin chain that maps to an interacting fermionic model. The nonequilibrium steady state exhibits surprising correlation effects, including an emergent pairing of hole excitations that arises from dynamically constrained hopping. Our system could be implemented in a number of experimental platforms, including circuit QED. Published by the American Physical Society 2024

Quark and lepton modular models from the binary dihedral flavor symmetry

Inspired by the structure of top-down derived models endowed with modular flavor symmetries, we investigate the yet phenomenologically unexplored binary dihedral group 2D3. After building the vector-valued modular forms in the representations of 2D3 with small modular weights, we systematically classify all (Dirac and Majorana) mass textures of fermions with fractional modular weights and all possible 2 + 1-family structures. This allows us to explore the parameter space of fermion models based on 2D3, aiming at a description of both quarks and leptons with a minimal number of parameters and best compatibility with observed data. We consider the separate possibilities of neutrino masses generated by either a type-I seesaw mechanism or the Weinberg operator. We identify a model that, besides fitting all known flavor observables, delivers predictions for six not-yet measured parameters and favors normal-ordered neutrino masses generated by the Weinberg operator. It would be interesting to figure out whether it is possible to embed our model within a top-down scheme, such as \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{T}}^{2}/{\\mathbb{Z}}_{4}$$\\end{document} heterotic orbifold compactifications.

Disentangling the physics of the attractive Hubbard model as a fully interacting model of fermions via the accessible and symmetry-resolved entanglement entropies

Disentangling the physics of the attractive Hubbard model as a fully interacting model of fermions via the accessible and symmetry-resolved entanglement entropies

Tensor renormalization group for fermions.

We review the basic ideas of the tensor renormalization group method and show how they can be applied for lattice field theory models involving relativistic fermions and Grassmann variables in arbitrary dimensions. We discuss recent progress for entanglement filtering, loop optimization, bond-weighting techniques and matrix product decompositions for Grassmann tensor networks. The new methods are tested with two-dimensional Wilson-Majorana fermions and multi-flavor Gross-Neveu models. We show that the methods can also be applied to the fermionic Hubbard model in 1+1 and 2+1 dimensions.

Thermalization of linear Fermi systems

The issue of thermalization in open quantum systems is explored from the perspective of fermion models with quadratic couplings and linear baths. Both the thermodynamic state and the stationary solution of the Lindblad equation are rendered as a matrix-product sequence following a reformulation in terms of underlying algebras, allowing to characterize a family of stationary solutions and determine the cases where they correspond to thermal states. This characterization provides insight into the operational mechanisms that lead the system to thermalization and their interplay with mechanisms that tend to drive it out of thermal equilibrium.

Designer Spin Models in Tunable Two-Dimensional Nanographene Lattices.

Motivated by recent experimental breakthroughs, we propose a strategy for designing two-dimensional spin-lattices with competing interactions that lead to nontrivial emergent quantum states. We consider S = 1/2 nanographenes with C3 symmetry as building blocks, and we leverage the potential to control both the sign and the strength of exchange with first neighbors to build a family of spin models. Specifically, we consider the case of a Heisenberg model in a triangle-decorated honeycomb lattice with competing ferromagnetic and antiferromagnetic interactions whose ratio can be varied in a wide range. On the basis of the exact diagonalization of both Fermionic and spin models, we predict a quantum phase transition between a valence bond crystal of spin singlets with triplon excitations living in a Kagomé lattice and a Néel phase of effective S = 3/2 in the limit of dominant ferromagnetic interactions.

Adiabatic Evolution of Low-Temperature Many-Body Systems

We consider finite-range, many-body fermionic lattice models and we study the evolution of their thermal equilibrium state after introducing a weak and slowly varying time-dependent perturbation. Under suitable assumptions on the external driving, we derive a representation for the average of the evolution of local observables via a convergent expansion in the perturbation, for small enough temperatures. Convergence holds for a range of parameters that is uniform in the size of the system. Under a spectral gap assumption on the unperturbed Hamiltonian, convergence is also uniform in temperature. As an application, our expansion allows us to prove closeness of the time-evolved state to the instantaneous Gibbs state of the perturbed system, in the sense of expectation of local observables, at zero and at small temperatures. As a corollary, we also establish the validity of linear response. Our strategy is based on a rigorous version of the Wick rotation, which allows us to represent the Duhamel expansion for the real-time dynamics in terms of Euclidean correlation functions, for which precise decay estimates are proved using fermionic cluster expansion.

Rotating black holes surrounded by a dark matter halo in the galactic center of M87 and Sgr A[formula omitted]

In this paper, we construct the solutions of modified Schwarzschild spacetime with three kinds of dark matter profiles, i.e. the Beta profiles, Moore profiles and Fermionic halos profiles. In order to make the models more realistic, by using the modified Newman–Janis algorithm (MNJA), we extend our solution to obtain three rotating black holes surrounded by dark matter halo and discuss the black hole properties such as the event horizon, ergoregion, geodesics of null particles and the black hole shadow. We consider two specific examples, i.e. using the present values for the parameters of the dark matter density profiles for the Sgr A∗ black hole and M87 central black hole, it shows that the effects of the dark matter on the size of shadows are almost negligible compared to the shadow of Kerr black hole. Besides, in specific condition having dark matter with very high density, we show that the shadow images of Beta model rotating black hole increase, but the shadow images of Moore model and Fermionic model rotating black holes decrease, furthermore, the Moore profile has the largest deviation, the Beta profile has the least deviation and the deviation of Fermionic halo model is in the middle. These phenomena may provides us with a possibility: the effect of dark matter on the apparent shadow shape could shed some light on mass density profiles of dark matter halo of a galaxy, by studying black holes in dark matter, it may provide an inspiration for us to indirectly detect dark matter.

Exploring entanglement characteristics in disordered free fermion systems through random bi-partitioning

This study investigates the entanglement properties of disordered free fermion systems undergoing an Anderson phase transition from a delocalized to a localized phase. The entanglement entropy is employed to quantify the degree of entanglement, with the system randomly divided into two subsystems. To explore this phenomenon, one-dimensional tight-binding fermion models and Anderson models in one, two, and three dimensions are utilized. Comprehensive numerical calculations reveal that the entanglement entropy, determined using random bi-partitioning, follows a volume-law scaling in both the delocalized and localized phases, expressed as [Formula: see text], where D represents the dimension of the system. Furthermore, the role of short and long-range correlations in the entanglement entropy and the impact of the distribution of subsystem sites are analyzed.

Exploring robust correlations between fermionic dark matter model parameters and neutron star properties: A two-fluid perspective

Exploring robust correlations between fermionic dark matter model parameters and neutron star properties: A two-fluid perspective

Remarks on discrete Dirac operators and their continuum limits

We discuss possible definitions of discrete Dirac operators, and discuss their continuum limits. It is well known in the lattice field theory that the straightforward discretization of the Dirac operator introduces unwanted spectral subspaces, and it is known as the fermion doubling . In oder to overcome this difficulty, two methods were proposed. The first one is to introduce a new term, called the Wilson term , and the second one is the KS-fermion model or the staggered fermion model . We discuss mathematical formulations of these, and study their continuum limits.