arXiv subjects

Stefan Kehrein

Publications and source records attributed to Stefan Kehrein.

At least 19 recordsLinked to original sources

arXiv2026

Sharp Page transitions in generic Hamiltonian dynamics

We consider the entanglement dynamics of a subsystem initialized in a pure state at high energy density (corresponding to negative temperature) and coupled to a cold bath. The subsystem's Rényi entropies $S_α$ first rise as the subsystem gets entangled with the bath and then fall as the subsystem cools. We find that the peak of the min-entropy, $\lim_{α\to \infty} S_α$, sharpens to a cusp in the thermodynamic limit at a well-defined time we call the Page time. We construct a hydrodynamic ansatz for the evolution of the entanglement Hamiltonian, which accounts for the sharp Page transition as well as the intricate dynamics of the entanglement spectrum before the Page time. Our results hold both when the bath has the same Hamiltonian as the system and when the bath is taken to be Markovian. Our ansatz suggests conditions under which the Page transition should remain sharp even for Rényi entropies of finite index $α$.

quant-ph↗

arXiv2026

Prethermal cooling with many-body quantum quenches

Many-body quantum quenches are typically associated with heating. In this work, we show that quantum quenches that perform positive work on the system can still lead to effective cooling of low-energy degrees of freedom if the quench energy is deposited in long-lived high-energy excitations. We discuss this explicitly for a quench of the hopping term t in the strong-coupling (U >> t) fermionic Hubbard model at half filling, where the quench induces a very long-lived non-equilibrium doublon density. The associated prethermal state persists for a time exponentially large in (U/t)^2. During this time window, we find an effective prethermal temperature that is reduced by the square of the ratio of final to initial hopping amplitude with respect to the initial temperature. This manifests as an effective fluctuation-dissipation relation that holds for doublon-number conserving operators. In a practical implementation the Hubbard system acts as a refrigerant to cool a target system provided the coupling conserves doublon number. Our protocol can be thought of as a quantum quench many-body generalization of adiabatic demagnetization.

quant-ph↗

arXiv2026

Resonant level model from a Krylov perspective: Lanczos coefficients in a quadratic model

We study the Lanczos coefficients in a quadratic model given by an impurity interacting with a multi-mode field of fermions, also known as resonant level model. We analytically derive closed expressions for the Lanczos coefficients of Majorana fermion operators of the impurity for different structures of the coupling to the hybridization band at zero temperature. While the model remains quadratic, we find that the growth of the Lanczos coefficients structurally depends strongly on the chosen coupling. Concretely, we find $(i)$ approximately constant, $(ii)$ exactly constant, $(iii)$ square root-like as well as $(iv)$ linear growth in the same model. We further argue that in fact through suitably chosen couplings, essentially arbitrary Lanczos coefficients can be obtained in this model. These altogether evince the inadequacy of the Lanczos coefficients as a reliable criterion for classifying the integrability or chaoticity of the systems. Eventually, in the wide-band limit, we find exponential decay of autocorrelation functions in all the settings $(i)-(iv)$, which demonstrates the different structures of the Lanczos coefficients not being indicative of different physical behavior.

cond-mat.str-el↗

arXiv2026

Extension of the Adiabatic Theorem

We examine the validity of a potential extension of the adiabatic theorem to quantum quenches, i.e., nonadiabatic changes. In particular, the transverse field Ising model (TFIM) and the axial next nearest neighbor Ising (ANNNI) model are studied. The proposed extension of the adiabatic theorem is stated as follows: Consider the overlap between the initial ground state and the postquench Hamiltonian eigenstates for quenches within the same phase. This overlap is largest for the postquench ground state. In the case of the TFIM, this conjecture is confirmed for both the paramagnetic and ferromagnetic phases numerically and analytically. In the ANNNI model, the conjecture could be analytically proven for a special case. Numerical methods were employed to investigate the conjecture's validity beyond this special case.

cond-mat.stat-mech↗

arXiv2026

Resonant level model coupled to a Sachdev-Ye-Kitaev bath

We investigate the non-equilibrium dynamics of a resonant level model coupled to a strongly interacting electron bath modeled by a Sachdev-Ye-Kitaev (SYK) model. Different from the well-investigated case of a structureless non-interacting Fermi gas bath leading to a temperature-independent exponential decay of the impurity orbital occupation, we find a temperature-dependent oscillatory decay. We attribute this difference to the lack of quasiparticles in the SYK model, which is reflected in its singular density of states at the Fermi level. Our results are exact and can be obtained analytically by mapping to a suitably structured Fermi gas bath as an ancillary model for the SYK bath.

cond-mat.str-el↗

arXiv2025

Rate Function Modelling of Quantum Many-Body Adiabaticity

The quantum adiabatic theorem is a fundamental result in quantum mechanics, with a multitude of applications, both theoretical and practical. Here, we investigate the dynamics of adiabatic processes for quantum many-body systems %in detail by analysing the properties of observable-free, intensive quantities. In particular, we study the adiabatic rate function $f(T, Δλ)$ in dependence of the ramp time $T$, which gives us a complete characterization of the many-body adiabatic fidelity as a function of $T$ and the strength of the parameter displacement $Δλ$. $f(T, Δλ)$ quantifies the deviation from adiabaticity for a given process and therefore allows us to control and define the notion of adiabaticity in many-body systems. First we study $f(T, Δλ)$ for the 1D transverse field Ising model and the Luttinger liquid, both of which are quadratic systems and therefore allow us to look at the thermodynamic limit. For ramps across gapped phases, we relate $f(T, Δλ)$ to the transition probability of the system and for ramps across a gapless point, or gapless phase we relate it to the excitation density of the relevant quasiparticles. Then we investigate the XXZ model which allows us to see the qualitative features that survive when interactions are turned on. Several key results in the literature regarding the interplay of the thermodynamic and the adiabatic limit are obtained as inferences from the properties of $f(T, Δλ)$ in the large $T$ limit.

quant-ph↗

arXiv2025

Page Curve and Entanglement Dynamics in an Interacting Fermionic Chain

Generic non-equilibrium many-body systems display a linear growth of bipartite entanglement entropy in time, followed by a volume law saturation. In stark contrast, the Page curve dynamics of black hole physics shows that the entropy peaks at the Page time $t_{\text{Page}}$ and then decreases to zero. Here, we investigate such Page-like behavior of the von Neumann entropy in a model of strongly correlated spinless fermions in a typical system-environment setup, and characterize the properties of the Page curve dynamics in the presence of interactions using numerically exact matrix product states methods. The two phases of growth, namely the linear growth and the bending down, are shown to be separated by a non-analyticity in the min-entropy before $t_{\text{Page}}$, which separates two different quantum phases, realized as the respective ground states of the corresponding entanglement (or equivalently, modular) Hamiltonian. We confirm and generalize, by introducing interactions, the findings of \href{https://journals.aps.org/prb/abstract/10.1103/PhysRevB.109.224308}{Phys. Rev. B 109, 224308 (2024)} for a free spinless fermionic chain where the corresponding entanglement Hamiltonian undergoes a quantum phase transition at the point of non-analyticity. However, in the presence of interactions, a scaling analysis gives a non-zero critical time for the non-analyticity in the thermodynamic limit only for weak to intermediate interaction strengths, while the dynamics leading to the non-analyticity becomes \textit{instantaneous} for interactions large enough. We present a physical picture explaining these findings.

quant-ph↗

arXiv2025

Thermalization of a Closed Sachdev-Ye-Kitaev System in the Thermodynamic Limit

The question of thermalization of a closed quantum system is of central interest in non-equilibrium quantum many-body physics. Here we present one such study analyzing the dynamics of a closed coupled Majorana SYK system. We have a large-$q$ SYK model prepared initially at equilibrium quenched by introducing a random hopping term, thus leading to non-equilibrium dynamics. We find that the final stationary state reaches thermal equilibrium with respect to the Green's functions and energy. Accordingly, the final state is characterized by calculating its final temperature and the thermalization rate. We provide a detailed review of analytical methods and derive the required Kadanoff-Baym equations, which are then solved using the algorithm developed in this work. Our results display rich thermalization dynamics in a closed quantum system in the thermodynamic limit.

cond-mat.str-el↗

arXiv2025

Universal quench dynamics of lattice $q$ fermion Yukawa Sachdev-Ye-Kitaev model

We study the quantum quench of the Yukawa Sachdev-Ye-Kitaev model and one of its lattice extensions with $q$ fermions and one boson. Several equilibrium properties are computed for general $q$ with different parameter scaling within the large-$N$ dynamical mean field scheme. The non-Fermi liquid quench dynamics are studied by integrating the Kadanoff-Baym equations for switching off the lattice term with constant Yukawa coupling or quenching to different final Yukawa couplings. The post-quench oscillations and relaxation dynamics are insensitive to the quench amplitudes deep inside the non-Fermi liquid phase. With weak lattice coupling quenches, we find universal thermalization dynamics similar to the SYK model; however, with two temperatures and two distinct relaxation rates for bosons and fermions, both signal Planckian relaxations without quasiparticles, as in strange metals.

cond-mat.str-el↗

arXiv2025

Current Correlations and Conductivity in SYK-Like Systems: An Analytical Study

We present a functional-based approach to compute thermal expectation values for actions expressed in the $G-Σ$ formalism, applicable to any time sequence ordering. Utilizing this framework, we analyze the linear response to an electric field in various Sachdev-Ye-Kitaev (SYK) chains. We consider the SYK chain where each dot is a complex $q/2$-body interacting SYK model, and we allow for $r/2$-body nearest-neighbor hopping where $r=κq$. We find exact analytical expressions in the large-$q$ limit for conductivities across all temperatures at leading order in $1/q$ for three cases, namely $κ= \{ 1/2, 1, 2\}$. When $κ= \{1/2, 1\}$, we observe linear-in-temperature $T$ resistivities at low temperatures, indicative of strange metal behavior. Conversely, when $κ= 2$, the resistivity diverges as a power law at low temperatures, namely as $1/T^2$, resembling insulating behavior. As $T$ increases, there is a crossover to Fermi liquid behavior ($\sim T^2$) at the minimum resistivity. Beyond this, another crossover occurs to strange metal behavior ($\sim T$). In comparison to previous linear-in-$T$ results in the literature, we also show that the resistivity behavior exists even below the MIR bound, indicating a true strange metal instead of a bad metal. In particular, we find for the $κ= 2$ case a smooth crossover from an insulating phase to a Fermi liquid behavior to a true strange metal and eventually becoming a bad metal as temperature increases. We extend and generalize previously known results on resistivities to all temperatures, do a comparative analysis across the three models where we highlight the universal features and invoke scaling arguments to create a physical picture out of our analyses. Remarkably, we find a universal maximum DC conductivity across all three models when the hopping coupling strength becomes large.

cond-mat.str-el↗

arXiv2024

Page curve entanglement dynamics in an analytically solvable model

The entanglement entropy of black holes is expected to follow the Page curve. After an initial linear increase with time the entanglement entropy should reach a maximum at the Page time and then decrease. This paper introduces an exactly solvable model of free fermions that explicitly shows such a Page curve: The entanglement entropy vanishes asymptotically for late times instead of saturating at a volume law. The bending down of the Page curve is accompanied by a breakdown of the semiclassical connection between particle current and entanglement generation, a quantum phase transition in the entanglement Hamiltonian and non-analytic behavior of the $q\rightarrow\infty$ Renyi entropy. These observations are expected to hold for a larger class of systems beyond the exactly solvable model analyzed here.

quant-ph↗

arXiv2024

Quench dynamics in higher-dimensional Holstein models: Insights from Truncated Wigner Approaches

Charge-density wave phases in quantum materials stem from the complex interplay of electronic and lattice degrees of freedom. Nowadays, various time-resolved spectroscopy techniques allow to actively manipulate such phases and monitor their dynamics in real time. Modeling such nonequilibrium dynamics theoretically is a great challenge and exact methods can usually only treat a small number of atoms and finitely many phonons. We approach the melting of charge-density waves in a Holstein model after a sudden switch-on of the electronic hopping from two perspectives: We prove that in the non-interacting and in the strong-coupling limit, the CDW order parameter on high-dimensional hypercubic lattices obeys a factorization relation for long times, such that its dynamics can be reduced to the one-dimensional case. Secondly, we present numerical results from semiclassical techniques based on the Truncated Wigner Approximation for two spatial dimensions. A comparison with exact data obtained for a Holstein chain shows that a semiclassical treatment of both the electrons and phonons is required in order to correctly describe the phononic dynamics. This is confirmed, in addition, for a quench in the electron-phonon coupling strength.

cond-mat.str-el↗

arXiv2024

Measurement-induced Clock in a Lattice Ring of Non-interacting Electrons

We examine the emergence of periodicity in a non-interacting steady-state quantum system without external drive inspired by quantum time crystals' spontaneous time-translation symmetry breaking. Specifically, we consider a lattice ring of non-interacting electrons undergoing weak local position measurements. Our analysis uncovers time-periodic structures in steady-state two-time correlation functions, with periodicity linked to the system's group velocity. This study demonstrates a measurement-induced clock mechanism, highlighting periodic behaviors in two-time correlators of a non-equilibrium steady state, contributing to understanding time-periodic phenomena in minimally interactive quantum systems.

quant-ph↗

arXiv2024

Systematic large flavor fTWA approach to interaction quenches in the Hubbard model

We study the nonequilibrium dynamics after an interaction quench in the two-dimensional Hubbard model using the recently introduced fermionic truncated Wigner approximation (fTWA). To assess the range of validity of the method in a systematic way, we consider the SU($N$) Hubbard model with the fermion degeneracy $N$ as a natural semiclassical expansion parameter. Using both a numerical and a perturbative analytical approach we show that fTWA is exact at least up to and including the prethermalization dynamics. We discuss the limitations of the method beyond this regime.

cond-mat.str-el↗

arXiv2023

The shared universality of charged black holes and the many many-body SYK model

We investigate the charged $q/2$-body interacting Sachdev-Ye-Kitaev (SYK) model in the grand-canonical ensemble. By treating $q$ as a large parameter, we are able to analytically study its phase diagram. By varying the chemical potential or temperature, we find that the system undergoes a phase transition between low and high entropies, in the maximally chaotic regime. A similar transition in entropy is seen in charged AdS black holes transitioning between a large and small event horizon. Approaching zero temperature, we find a first-order chaotic-to-non-chaotic quantum phase transition, where the finite extensive entropy drops to zero. This again has a gravitational analogue -- the Hawking-Page (HP) transition between a large black hole and thermal radiation. An analytical study of the critical phenomena associated with the continuous phase transition provides us with mean field van der Waals critical and effective exponents. We find that all analogous power laws are shared with several charged AdS black hole phase transitions. Together, these findings indicate a connection between the charged $q\to\infty$ SYK model and black holes.

cond-mat.str-el↗

arXiv2022

Photoinduced prethermal order parameter dynamics in the two-dimensional large-$N$ Hubbard-Heisenberg model

We study the microscopic dynamics of competing ordered phases in a two-dimensional correlated electron model, which is driven with a pulsed electric field of finite duration. In order to go beyond a mean-field treatment of the electronic interactions we adopt a large-$N$ generalization of the Hubbard model and combine it with the semiclassical fermionic truncated Wigner approximation as a time evolution method. This allows us to calculate dephasing corrections to the mean-field dynamics and to obtain stationary states, which we interpret as prethermal order. We use this framework to simulate the light-induced transition between two competing phases (bond density wave and staggered flux) and find that the post-pulse stationary state order parameter values are not determined alone by the amount of absorbed energy but depend explicitly on the driving frequency and field direction. While the transition between the two prethermal phases takes place at similar total energies in the low- and high-frequency regimes, we identify an intermediate frequency regime for which it occurs with minimal heating.

cond-mat.str-el↗

arXiv2022

Scrambling and Many-Body Localization in the XXZ-Chain

The tripartite information is an observable-independent measure for scrambling and delocalization of information. Therefore one can expect that the tripartite information is a good observable-independent indicator for distinguishing between many-body localized and delocalized regimes, which we confirm for the XXZ-chain in a random field. Specifically, we find that the tripartite information signal spreads inside a lightcone that only grows logarithmically in time in the many-body localized regime similar to the entanglement entropy. We also find that the tripartite information eventually reaches a plateau with an asymptotic value that is suppressed by strong disorder.

cond-mat.dis-nn↗

arXiv2022

Thermalization of many many-body interacting SYK models

We investigate the non-equilibrium dynamics of complex Sachdev-Ye-Kitaev (SYK) models in the $q\rightarrow\infty$ limit, where $q/2$ denotes the order of the random Dirac fermion interaction. We extend previous results by Eberlein et al. [Phys. Rev. B 96, 205123 (2017)] to show that a single SYK $q\rightarrow\infty$ Hamiltonian for $t\geq 0$ is a perfect thermalizer in the sense that the local Green's function is instantaneously thermal. The only memories of the quantum state for $t<0$ are its charge density and its energy density at $t=0$. Our result is valid for all quantum states amenable to a~$1/q$-expansion, which are generated from an equilibrium SYK state in the asymptotic past and acted upon by an arbitrary combination of time-dependent SYK Hamiltonians for $t<0$. Importantly, this implies that a single SYK $q\rightarrow\infty$ Hamiltonian is a perfect thermalizer even for non-equilibrium states generated in this manner.

cond-mat.str-el↗