We use the Schrieffer-Wolff transformation (SWT) to analyze Josephson junctions between superconducting leads described by the charge-conserving BCS theory. Starting from the single-electron tunneling terms, we directly recover the conventional effective Hamiltonian, -EJ cos phi, with an operator-valued phase bias phi. The SWT approach has the advantage that it can be systematically extended to more complex scenarios. We show that if a Bogoliubov quasiparticle is present its motion couples to that of Cooper pairs, introducing correlated dynamics that reshape the energy spectrum of the junction. Furthermore, higher-order terms in the SWT naturally describe Josephson harmonics, whose amplitudes are directly related to the microscopic properties of the superconducting leads and the junction. We derive expressions that could facilitate tuning the ratio between the different harmonics in a controlled way.

We study the spin-partitioned entanglement Hamiltonian of the one-dimensional repulsive Hubbard model. By combining bosonization with exact diagonalization, we show that tracing out one spin species produces a modular Luttinger liquid, whose properties fundamentally differ from those of the physical system. While the modular spectrum is fully dispersionless and possesses a momentum-independent entanglement gap, its eigenstates exhibit algebraic correlations governed by a single effective Luttinger parameter equal to the geometric mean of the charge and spin Luttinger parameters. The resulting entanglement spectrum displays a universal branching hierarchy in excellent agreement with exact diagonalization. We further demonstrate that the modular ground state is nearly identical to that of the spinless Luttinger liquid. These results uncover a universal modular structure in interacting one-dimensional fermionic systems.

We investigate the interplay between altermagnetic band structures and electronic correlations by focusing on the d_x^2-y^2 altermagnetic generalization of the Hatsugai-Kohmoto model. We find that with increasing interaction, a many-body Lifshitz transition takes place when doubly occupied regions disappear from the Fermi surface and almost all momentum states become fully spin polarized. This is termed interaction enhanced altermagnet. We find that the dynamical susceptibility, which possesses only transverse non-zero components for small wavevectors, develops a gap proportional to the interaction strength, and displays a sharp peak at a frequency increasing with the interaction. Above the Lifshitz transition, this peak moves to the lower gap edge and becomes log-divergent. The signal intensity increases with the interaction up until the Lifshitz transition and saturates afterwards. The static susceptibility remains unaffected by the correlations and altermagnetism reduces the static transverse response.

We focus on the infinite temperature dynamical spin structure factor of the asymmetric Hatsugai-Kohmoto model, the relative of the asymmetric Hubbard model. It is characterized by distinct single particle energies for the two spin species, which interact with each other through a contact interaction in momentum space. We evaluate its spin structure factor exactly and follow the evolution of its excitation spectrum for all fillings and interactions, identify signatures of the Mott transition and fingerprints of the asymmetric hoppings. The longitudinal spin structure factor exhibits sound like and interaction induced gapped excitations, whose number gets doubled in the presence of hopping asymmetry. The transverse response displays the competition of interaction and asymmetry induced gaps and results in a quadratic excitation branch at their transition. The complete asymmetric case features momentum-independent dynamical structure factor, characteristic to transitions involving a flat band.

We study the nonequilibrium dynamics of the superconducting order parameter in the Hatsugai-Kohmoto (HK) model. In the absence of superconductivity, its ground state is a non-Fermi liquid, whose properties are controlled by the HK interaction. Our protocol involves quantum quenching the HK interaction but leaving the interaction responsible for superconductivity unchanged. We map out the nonequilibrium dynamical phase diagram of the interacting model which contains three phases where, at long times, the order parameter amplitude vanishes, approaches a constant value, or persistently oscillates. We also investigate the Loschmidt echo in searching for dynamical quantum phase transition and find that its nonanalytic temporal behavior is close but does not match exactly the vanishing of the order parameter. The momentum space entanglement entropy between positive and negative momentum modes, relevant for Cooper pairing, is calculated. Counterintuitively, this momentum space entanglement does not change significantly during the quench dynamics and its value remains reasonably large even for a vanishing superconducting order parameter. Nevertheless, its derivative with respect to the HK interaction signals the dynamical phase transition associated to the late time vanishing of superconductivity.

An electron tunneling across a junction integrated into an electric circuit can generate an excitation in the photonic field (electromagnetic environment) and lose energy in the process. Such inelastic tunneling of particles is commonly described using the P ( E ) theory. In the conventional approach to this theory, the tunneling rate and the electric current through the junction are derived using Fermi's golden rule and by averaging over the environmental photonic degrees of freedom. In this work, we address the same problem of inelastic tunneling due to photonic environment in Lindbladian formalism and we present how the photonic degrees of freedom are traced out in the quantum master equation approach. The resulting quantum master equation is parametrized by the same P ( E ) function and enables us to obtain not only the electric current but various other quantities, for instance, the heat current, in a systematic and convenient way. We also demonstrate that the Lindbladian formalism provides a comprehensive description of Bogoliubov quasiparticle tunneling through superconducting junctions and that it properly accounts for the coherence factors. The coherence factors become important if the normal-state density of states is particle-hole asymmetric.

We present a theoretical study of a system consisting of a superconducting island and two quantum dots, a possible platform for building qubits and Cooper pair splitters, in the regime where each dot hosts a single electron and, hence, carries a magnetic moment. We focus on the case where the dots are coupled to overlapping superconductor states and we study whether the spins are ferromagnetically or antiferromagnetically aligned. We show that if the total number of particles is even, the spins align antiferromagnetically in the flatband limit, i.e., when the bandwidth of the superconductor is negligibly small, but ferromagnetically if the bandwidth is finite and above some value. If the total number of particles is odd, the alignment is ferromagnetic independently from the bandwidth. This implies that the results of the flatband limit are applicable only within restricted parameter regime for realistic superconducting qubit systems and that some care is required in applying simplified models to devices such as Cooper pair splitters.

We study the autonomous systems of quadratic differential equations of the form $${\dot{x}}_i(t)={\textbf{x}}(t)^T {\textbf{A}}_i {\textbf{x}}(t) + {\textbf{v}}_i^T {\textbf{x}}(t)$$ with $${\textbf{x}}(t) = (x_1(t),$$ $$x_2(t), \ldots ,x_i(t),\dots )$$ which, in general, cannot be solved exactly. In the present paper, we introduce a subclass of analytically solvable quadratic systems, whose solution is realized through a multi-dimensional generalization of the inversion which transforms a quadratic system into a linear one. We provide a constructive algorithm which, on one hand, decides whether the system of differential equations is analytically solvable with the inversion transformation and, on the other hand, provides the solution. The presented results apply for arbitrary, finite number of variables.

The Kibble-Zurek mechanism describes defect production due to non-adiabatic passage through a critical point. Here we study its variant from ramping the environment temperature to a critical point. We find that the defect density scales as [Formula: see text] or [Formula: see text] for thermal or quantum critical points, respectively, in terms of the usual critical exponents and [Formula: see text] the speed of the drive. Both scalings describe reduced defect density compared to conventional Kibble-Zurek mechanism, which stems from the enhanced relaxation due to bath-system interaction. Ramping to the quantum critical point is investigated by studying the Lindblad equation for the transverse field Ising chain in the presence of thermalizing bath, with couplings to environment obeying detailed balance, confirming the predicted scaling. The von-Neumann or the system-bath entanglement entropy follows the same scaling. Our results are generalized to a large class of dissipative systems with power-law energy dependent bath spectral densities as well.

We study the nonequilibrium dynamics of a Luttinger liquid after a simultaneous quantum quench of the interaction and dissipative quench to the environment within the realm of the Lindblad equation. When the couplings to the environment satisfy detailed balance, the system is destined to thermalize, which we follow using bosonization. The thermodynamic entropy of the system, which also encodes information about the entanglement with the environment, either exhibits a maximum and minimum or grows monotonically before reaching its thermal value in a universal fashion. The single-particle density matrix reveals interesting features in the spatiotemporal "phase diagram," including thermal, prethermal, and dissipation enhanced sudden quench Luttinger liquid behavior, as well as dissipation, enhanced Fermi liquid response.

We study the dissipative dynamics of one-dimensional fermions, described in terms of the sine-Gordon model in its free massive boson or semi-classical limit, while keeping track of forward scattering processes. The system is prepared in the gapped ground state, and then coupled to environment through local currents within the Lindblad formalism. The heating dynamics of the system is followed using bosonization. The single particle density matrix exhibits correlations between the left and right moving particles. While the density matrix of right movers and left movers is translationally invariant, the left-right sector is not, corresponding to a translational symmetry breaking charge density wave state. Asymptotically, the single particle density matrix decays exponentially with exponent proportional to -\gamma t|x|\Delta^2−γt|x|Δ2 where \gammaγ and \DeltaΔ are the dissipative coupling and the gap, respectively. The charge density wave order parameter decays exponentially in time with an interaction independent decay rate. The second R'enyi entropy grows linearly with time and is essentially insensitive to the presence of the gap.

We study the non-equilibrium dynamics of a Luttinger liquid after a simultaneous quantum quench of the interaction and dissipative quench to the environment within the realm of the Lindblad equation. When the couplings to environment satisfy detailed balance, the system is destined to thermalize, which we follow using bosonization. The thermodynamic entropy of the system, which also encodes information about the entanglement with the environment, either exhibits a maximum and minimum or grows monotonically before reaching its thermal value in a universal fashion. The single-particle density matrix reveals rich behaviour in the spatio-temporal "phase diagram", including thermal, prethermal and dissipation enhanced sudden quench Luttinger liquid behaviour as well as dissipation enhanced Fermi liquid response.

Ádám Bácsi, 2, ∗ Cătălin Paşcu Moca, 4 Gergely Zaránd, 5 and Balázs Dóra 6 MTA-BME Lendület Topology and Correlation Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary Department of Mathematics and Computational Sciences, Széchenyi István University, 9026 Győr, Hungary MTA-BME Quantum Dynamics and Correlations Research Group, Budapest University of Technology and Economics, 1521, Budapest, Hungary Department of Physics, University of Oradea, 410087, Oradea, Romania BME-MTA Exotic Quantum Phases Research Group, Department of Theoretical Physics, Budapest University of Technology and Economics, Budapest, Hungary Department of Theoretical Physics, Budapest University of Technology and Economics, Budapest, Hungary (Dated: August 13, 2021)

We investigate a quantum quench from a critical to an exceptional point. The initial state, prepared in the ground state of a critical Hermitian system, is time evolved with a non-Hermitian SSH model, tuned to its exceptional point. The single particle density matrix exhibits supersonic modes and multiple light cones, characteristic of non-Hermitian time evolution. These propagate with integer multiples of the original Fermi velocity. In the long time limit, the fermionic Green's function decays spatially as 1/x(2), in sharp contrast to the usual 1/x decay of noninteracting fermions. The entanglement entropy is understood as if all these supersonic modes arise from independent quasiparticles (though they do not), traveling with the corresponding supersonic light cone velocity. The entropy production rate decreases with time and develops plateaus during the time evolution, signaling the distinct velocities in the propagation of nonlocal quantum correlations. At late times, the entanglement entropy saturates to a finite value, satisfying a volume law.

We study a one-dimensional Fermi gas in the presence of dissipative coupling to environment through the Lindblad equation. The dissipation involves energy exchange with the environment and favours the relaxation of electrons to excitations. After switching on the dissipation, the system approaches a steady state, which is described by a generalized Gibbs ensemble. The fermionic single particle density matrix resembles deceivingly to that in a hermitian interaction quench. It decays inversely with the distance for short times due to the fermionic correlations in the initial state, which changes into a noninteger power law decay for late times, representing dissipation-induced Luttinger liquid behavior. However, the crossover between the two regions occurs due to dissipation-induced damping, and is unrelated to the propagation of excitations. The velocity of information spreading is set by the dissipative coupling, and differs significantly from the original sound velocity. The thermodynamic entropy grows as -t ln t initially, and saturates to an extensive value. Our results can be tested experimentally in one-dimensional Dirac systems.

We investigate the stability of a Luttinger liquid, upon suddenly coupling it to a dissipative environment. Within the Lindblad equation, the environment couples to local currents and heats the quantum liquid up to infinite temperatures. The single particle density matrix reveals the fractionalization of fermionic excitations in the spatial correlations by retaining the initial noninteger power law exponents, accompanied by an exponential decay in time with an interaction dependent rate. The spectrum of the time evolved density matrix is gapped, which collapses gradually as -ln(t). The von Neumann entropy crosses over from the early time -tln(t) behavior to ln(t) growth for late times. The early time dynamics is captured numerically by performing simulations on spinless interacting fermions, using several numerically exact methods. Our results could be tested experimentally in bosonic Luttinger liquids.

Reaching a target quantum state from an initial state within a finite temporal window is a challenging problem due to nonadiabaticity. We study the optimal protocol for switching on interactions to reach the ground state of a weakly interacting Luttinger liquid within a finite time $\ensuremath{\tau}$, starting from the noninteracting ground state. The protocol is optimized by minimizing the excess energy at the end of the quench, or by maximizing the overlap with the interacting ground state. We find that the optimal protocol is symmetric with respect to $\ensuremath{\tau}/2$, and can be expressed as a functional of the occupation numbers of the bosonic modes in the final state. For short quench durations, the optimal protocol exhibits fast oscillation and excites high-energy modes. In the limit of large $\ensuremath{\tau}$, minimizing energy requires a smooth protocol while maximizing overlap requires a linear quench protocol. In this limit, the minimal energy and maximal overlap are both universal functions of the system size and the duration of the protocol.

Unsteady heat transfer processes between a heat source and the environment are completely described by the frequency-dependent heat transmission matrix within linear response theory. The 2 x 2 matrix characterizes the linear relation between the temperature and the heat transfer rate at the heat source and the environment sides of the system. In generic case, the heat transmission matrix has four independent complex entries. The number of independent elements may be reduced in the presence of certain properties or symmetries of the system. In the present paper, it is shown how the microscopic, governing equations influence whether the heat transmission matrix has a determinant of unity. A determinant fixed to one allows only three independent elements of the matrix. In the presence of a spatial symmetry under which the roles of the heat source and the environment are changed, the number of independent entries is reduced to two. The two independent elements may be formulated in terms of an effective thermal resistance and an effective heat capacity. In the case of a heat conducting wall, the effective values are independent of the frequency and equal to the static thermal resistance and heat capacity of the system. For generic symmetric systems, however, the effective thermal resistance and heat capacity may exhibit significant frequency dependence. The frequency dependence is numerically studied in the example of the heat conduction between two parallel pipes.

We study the nonequilibrium dynamics of the Luttinger model after a quantum quench, when the initial state is a finite temperature thermal equilibrium state. The diagonal elements of the density matrix in the steady state show thermal features for high temperature initial states only, otherwise they retain highly nonthermal character. The time evolution of Uhlmann fidelity, which measures the distance between the time evolved and initial states, is evaluated for arbitrary initial temperatures and quench protocols. In the long time limit, the overlap between the time evolved and initial system decreases exponentially with the temperature with a universal prefactor. Within perturbation theory, the statistics of final total energy and work are numerically evaluated in the case of a sudden quench, which yield identical distributions at zero temperature. In both statistics, temperature effects are more significant in small systems. The Dirac-delta peak at the adiabatic ground state energy remains present in the probability distribution of the total energy, but disappears from the work distribution at nonzero initial temperatures.