Fermion Systems Research Articles

Ultrafast optical induction of magnetic order at a quantum critical point

Time-resolved ultrafast spectroscopy has emerged as a promising tool to dynamically induce and manipulate non-trivial electronic states of matter out-of-equilibrium. Here we theoretically investigate light pulse driven dynamics in a Kondo lattice system close to quantum criticality. Based on a time-dependent auxiliary fermion mean-field calculation we show that light can dehybridize the local Kondo screening and induce oscillating magnetic order out of a previously paramagnetic state. Depending on the laser pulse field amplitude and frequency the Kondo singlet can be completely deconfined, inducing a dynamic Lifshitz transition that changes the Fermi surface topology. These phenomena can be identified in harmonic generation and time-resolved angle-resolved photoemission spectroscopy spectra. Our results shed new light on non-equilibrium states in heavy fermion systems.

Monitored fermions with conserved U(1) charge

We study measurement-induced phases of free fermion systems with U(1) symmetry. Following a recent approach developed for Majorana chains, we derive a field theory description for the purity and bipartite entanglement at large space and timescales. We focus on a multiflavor one-dimensional chain with random complex hoppings and continuous monitoring of the local fermion density. By means of the replica trick, and using the number of flavors as a large parameter controlling our approximations, we derive an effective field theory made up of a SU(N) nonlinear sigma model (NLσM) coupled to fluctuating hydrodynamics. Contrary to the case of noninteracting Majorana fermions, displaying no U(1) symmetry, we find that the bipartite entanglement entropy satisfies an area law for all monitoring rates but with a nontrivial scaling of entanglement when the correlation length is large. We provide numerical evidence supporting our claims. We briefly show how imposing a reality condition on the hoppings can change the NLσM and also discuss higher-dimensional generalizations. Published by the American Physical Society 2024

Scrambling transition in free fermion systems induced by a single impurity

Scrambling transition in free fermion systems induced by a single impurity

Qudit-based quantum simulation of fermionic systems

Model Hamiltonians described by fermionic operators are ubiquitous in physics and chemistry, but the quantum simulation of their properties is challenging on near-term quantum computers. Indeed, for any problem with more than two connected neighbors, standard mappings of fermions on qubits lead to many-body operators whose size increases with the size of the problem, quickly making the simulation unfeasible on noisy devices. Here we consider an alternative mapping based on qudits and the auxiliary fermion method, which leads to a significant reduction in the circuit depth and in the number of computational units to be controlled. These advantages increase for highly connected target Hamiltonians, such as lattices with long-range interactions or the molecular systems investigated in quantum chemistry. We numerically test our approach on qudits encoded in molecular spins, by performing the quantum simulation of a fermionic model on a small cluster. Published by the American Physical Society 2024

Boundary Strichartz estimates and pointwise convergence for orthonormal systems

AbstractWe consider maximal estimates associated with fermionic systems. Firstly, we establish maximal estimates with respect to the spatial variable. These estimates are certain boundary cases of the many‐body Strichartz estimates pioneered by Frank, Lewin, Lieb and Seiringer. We also prove new maximal‐in‐time estimates, thereby significantly extending work of Lee, Nakamura and the first author on Carleson's pointwise convergence problem for fermionic systems.

Modification of Premises for the Black Hole Information Paradox Caused by Topological Constraints in the Event Horizon Vicinity

We demonstrate that at the rim of the photon sphere of a black hole, the quantum statistics transition takes place in any multi-particle system of indistinguishable particles, which passes through this rim to the inside. The related local departure from Pauli exclusion principle restriction causes a decay of the internal structure of collective fermionic systems, including the collapse of Fermi spheres in compressed matter. The Fermi sphere decay is associated with the emission of electromagnetic radiation, taking away the energy and entropy of the falling matter without unitarity violation. The spectrum and timing of the related e-m radiation agree with some observed short giant gamma-ray bursts and X-ray components of the luminosity of quasars and of short transients powered by black holes. The release of energy and entropy when passing the photon sphere rim of a black hole significantly modifies the premises of the information paradox at the falling of matter into a black hole.

Exactly Solvable Inhomogeneous Fermion Systems

Abstract 15 exactly solvable inhomogeneous (spinless) fermion systems on 1D lattices are constructed explicitly based on the discrete orthogonal polynomials of the Askey scheme, e.g. Krawtchouk, Hahn, Racah, Meixner, and q-Racah polynomials. The Schrödinger and Heisenberg equations are solved explicitly, as the entire set of the eigenvalues and eigenstates are known explicitly. The ground-state two-point correlation functions are derived explicitly. The multipoint correlation functions are obtained by Wick’s theorem. 15 corresponding exactly solvable XX spin systems are also displayed. They all have nearest-neighbor interactions. The exact solvability of the Schrödinger equation means that the corresponding Fokker–Planck equation is also exactly solvable. This leads to 15 exactly solvable birth and death fermions and 15 birth and death spin models. These provide plenty of material for calculating interesting quantities, e.g. entanglement entropy, etc.

Baryogenesis in Minkowski spacetime

Based on a mechanism originally suggested for causal fermion systems, the present paper paves the way for a rigorous treatment of baryogenesis in the language of differential geometry and global analysis. Moreover, a formula for the rate of baryogenesis in Minkowski spacetime is derived.

Higher-bracket structure of density operators in Weyl fermion systems and topological insulators

Higher-bracket structure of density operators in Weyl fermion systems and topological insulators

Speed limits to fluctuation dynamics

Fluctuation dynamics of an experimentally measured observable offer a primary signal for nonequilibrium systems, along with dynamics of the mean. While universal speed limits for the mean have actively been studied recently, constraints for the speed of the fluctuation have been elusive. Here, we develop a theory concerning rigorous limits to the rate of fluctuation growth. We find a principle that the speed of an observable’s fluctuation is upper bounded by the fluctuation of an appropriate observable describing velocity, which also indicates a tradeoff relation between the changes for the mean and fluctuation. We demonstrate the advantages of our inequalities for processes with non-negligible dispersion of observables, quantum work extraction, and the entanglement growth in free fermionic systems. Our results open an avenue toward a quantitative theory of fluctuation dynamics in various non-equilibrium systems encompassing quantum many-body systems and nonlinear population dynamics.

Weyl laws for interacting particles

We study grand-canonical interacting fermionic systems in the mean-field regime, in a trapping potential. We provide the first order term of integrated and pointwise Weyl laws, but in the case with interaction. More precisely, we prove the convergence of the densities of the grand-canonical Hartree-Fock ground state to the Thomas-Fermi ground state in the semiclassical limit ℏ → 0. For the proof, we write the grand-canonical version of the results of Fournais, Lewin, and Solovej [Calculus Var. Partial Differ. Equations 57, 105 (2018)] and Conlon [Commun. Math. Phys. 88, 133 (1983)].

Multiple crossings during dynamical symmetry restoration and implications for the quantum Mpemba effect

Abstract Local relaxation after a quench in 1D quantum many-body systems is a well-known and very active problem with rich phenomenology. Except in pathological cases, the local relaxation is accompanied by the local restoration of the symmetries broken by the initial state that are preserved by unitary evolution. Recently, the entanglement asymmetry has been introduced as a probe to study the interplay between symmetry breaking and relaxation in an extended quantum system. In particular, using the entanglement asymmetry, it has been shown that the more a symmetry is initially broken, the faster it may be restored. This surprising effect, which has also been observed in trapped-ion experiments, can be seen as a quantum version of the Mpemba effect, and is manifested by the crossing at a finite time of the entanglement asymmetry curves of two different initial symmetry-breaking configurations. In this paper we show that, by tuning the initial state, the symmetry dynamics in free fermionic systems can display much richer behavior than seen previously. In particular, for certain classes of initial states, including the ground states of free fermionic models with long-range couplings, the entanglement asymmetry can exhibit multiple crossings. This illustrates that the existence of the quantum Mpemba effect can only be inferred by examining the late-time behavior of the entanglement asymmetry.

Orthogonality catastrophe beyond bosonization from post-selection

We show that the dynamics induced by post-selected measurements can serve as a controlled route to access physical processes beyond the boundaries of Luttinger liquid physics. We consider a one-dimensional fermionic wire whose dynamics results from a sequence of weak measurements of the fermionic density at a given site, interspersed with unitary hopping dynamics. This realizes a non-Hermitian variant of the celebrated instance of a local scatterer in a fermionic system and its ensuing orthogonality catastrophe. We observe a distinct crossover in the system's time evolution as a function of the fermion density. In the high-density regime, reminiscent of the Hermitian case, a bosonized version of the model properly describes the dynamics while, as we delve into the low-density regime, the validity of bosonization breaks down, giving rise to irreversible behavior. Notably, this crossover from reversible to irreversible dynamics is nonperturbative in the measurement rate and can manifest itself even with relatively shallow measurement rates, provided that the system's density remains below the crossover threshold. Our results render a conceptually transparent model for exploring nonperturbative effects beyond bosonization, which could be used as a stepping stone to explore novel routes for the control of nonlinear dynamics in low-dimensional quantum systems. Published by the American Physical Society 2024

Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations.

Developing numerical exact solvers for open quantum systems is a challenging task due to the non-perturbative and non-Markovian nature when coupling to structured environments. The Feynman-Vernon influence functional approach is a powerful analytical tool to study the dynamics of open quantum systems. Numerical treatments of the influence functional including the quasi-adiabatic propagator technique and the tensor-network-based time-evolving matrix product operator method have proven to be efficient in studying open quantum systems with bosonic environments. However, the numerical implementation of the fermionic path integral suffers from the Grassmann algebra involved. In this work, we present a detailed introduction to the Grassmann time-evolving matrix product operator method for fermionic open quantum systems. In particular, we introduce the concepts of Grassmann tensor, signed matrix product operator, and Grassmann matrix product state to handle the Grassmann path integral. Using the single-orbital Anderson impurity model as an example, we review the numerical benchmarks for structured fermionic environments for real-time nonequilibrium dynamics, real-time and imaginary-time equilibration dynamics, and its application as an impurity solver. These benchmarks show that our method is a robust and promising numerical approach to study strong coupling physics and non-Markovian dynamics. It can also serve as an alternative impurity solver to study strongly correlated quantum matter with dynamical mean-field theory.

Time-reversal anomalies of QCD3 and QED3

Anomalies of global symmetry provide powerful tool to constrain the dynamics of quantum systems, such as anomaly matching in the renormalization group flow and obstruction to symmetric mass generation. In this note we compute the anomalies in 2+1d time-reversal symmetric gauge theories with massless fermions in the fundamental and rank-two tensor representations, where the gauge groups are SU(N), SO(N), Sp(N), U(1). The fermion parity is part of the gauge group and the theories are bosonic. The time-reversal symmetry satisfies T2 = 1 or T2 = M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{M} $$\\end{document} where M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{M} $$\\end{document} is an internal magnetic symmetry. We show that some of the bosonic gauge theories have time-reversal anomaly with c− ≠ 0 mod 8 that is absent in fermionic systems. The anomalies of the gauge theories can be nontrivial even when the number of Majorana fermions is a multiple of 16 and ν = 0.

Entanglement entropy in ground states of long-range fermionic systems

Entanglement entropy in ground states of long-range fermionic systems

Floquet engineering of a dynamical Z2 lattice gauge field with ultracold atoms

Abstract Gauge field theory is a fundamental concept in modern physics, attracting many theoretical and experimental efforts towards its simulation. In this paper we propose that a simple model, in which fermions coupled to a dynamical lattice gauge field, can be engineered via the Floquet approach. The model possesses both an independent Maxwell term and local Z 2 gauge symmetry. Our proposal relies on a species-dependent optical lattice, and can be achieved in one, two or three dimensions. By a unitary transformation, this model can be mapped into a non-interacting composite fermion system with fluctuating background charge. With the help of this composite fermion picture, two characteristic observations are predicted. One is radio-frequency spectroscopy, which exhibits no dispersion in all parameter regimes. The second is dynamical localization, which depends on the structure of the initial states.

Non-hermitian Dirac theory from Lindbladian dynamics

This study investigates the intricate relationship between dissipative processes of open quantum systems and the non-Hermitian quantum field theory of relativistic fermionic systems. By examining the influence of dissipative effects on Dirac fermions via Lindblad formalism, we elucidate the effects of coupling relativistic Dirac particles with the environment and show the lack of manifest Lorentz invariance. Employing rigorous theoretical analysis, we generalize the collisionless Boltzmann equations for the relativistic dissipation-driven fermionic system and find the Lyapunov equation, which governs the stationary solutions. Using our formalism, one presents a simple non-Hermitian model that the relativistic fermionic particles and anti-particles are stable. Going further, using the solution to the Lyapunov equations, one analyses the effect of dissipation on the stationary charge imbalance of this non-Hermitian model and finds that the dissipation can induce a new kind of charge imbalance compared with the collisionless equilibrium case.

Fully polarized Fermi systems at finite temperature.

We propose a simple model of an interacting, fully spin-polarized Fermi gas in dimensions d=2 and d=3, and derive the approximate expression for the energy spectrum and the corresponding formula for the Helmholtz free energy. We analyze the thermodynamics of the system and find the lines of first-order phase transitions between the low- and high-density phases terminating at critical points. The properties of the corresponding phase diagrams are qualitatively different for d=2 and 3, and sensitively depend on the interparticle attraction, which marks a departure from the standard van der Waals theory. The differences originate from the Pauli exclusion principle and are embedded in the fermionic nature of the system under study.

Causal Fermion Systems and Octonions

AbstractThe authors compare the structures and methods in the theory of causal fermion systems with approaches to fundamental physics based on division algebras, in particular the octonions. It is found that octonions and, more generally, tensor products of division algebras come up naturally to describe the symmetries of the vacuum configuration of a causal fermion system. This is achieved by associating the real and imaginary octonion basis elements with the neutrino and charged sectors of the vacuum fermionic projector, respectively. Conversely, causal fermion systems provide octonionic theories with spacetime structures and dynamical equations via the causal action principle. In this way, octonionic theories and causal fermion systems complement each other.