One conception of a dynamical quantum phase transition (DQPT) is the
appearance of non-analyticies in the return rate (Loschmidt Echo), which is the overlap of an initial state at t=0 with a time-evolved state at time t with respect to a global quench. I will present an algorithm for calculating the moments of the return rate for translationally invariant infinite MPS, which is expressed in terms of the spectrum of the mixed transfer matrix. This leads naturally to analogues of Fisher and Lee-Yang zeros for the return rate and a topological interpretation/classification of DQPT's.
I will discuss the effects of different symmetry-breaking and long-range interactions on the stability of topologically nontrivial magnetic excitations. SU(N) magnets. Specifically, I will address the stability of skyrmions in presence of anisotropy and RKKY interactions, and topological multipletting of skyrmions and monopoles in SU(N) antiferromagnets.
Tensor network ansätze have been established as a method to overcome the exponential growth of the Hilbert space and still have a quasi-exact representation of quantum many-body wave functions.
I will begin with a pedagogical introduction to Matrix Product States (MPS) and the famous Density Matrix Renormalization Group (DMRG) algorithm.
In the second half, I will give an overview of the TeNPy code library and demonstrate examples how to call DMRG and other MPS-based algorithms.
A zoom stream will be available on
https://uni-goettingen.zoom.us/j/96249516311?pwd=Q2tURDFpcUVQaEQ3cXJSVk9wNkFPQT09
for those unable to attend "live".
Conformal field theories are naturally defined on compact Riemann surfaces. The rational ones can be solved using methods from algebraic geometry. One particular feature is the covariance of the partition function under the mapping class group. For the (2,5) minimal model and in genus one, one obtains a second order ODE of hypergeometric type, whose solutions are given by the Rogers-Ramanujan functions. One way to extend the theory to higher genus is by sewing tori. Alternatively, our algebraic description allows to deal with all genera at once (joint work with Werner Nahm).
Tensor product states are powerful tools for simulating area-law entangled states of many-body systems. The applicability of such methods to the non-equilibrium dynamics of many-body systems is less clear due to the presence of large amounts of entanglement. New methods seek to reduce the numerical cost by selectively discarding those parts of the many-body wavefunction, which are thought to have relatively litte effect on dynamical quantities of interest. We present a theory for the sizes of “backflow corrections”, i.e., systematic errors due to these truncation effects and introduce the dissipation-assisted operator evolution (DAOE) method for calculating transport properties of strongly interacting lattice systems in the high temperature regime. In the DAOE method, we represent the observable as a matrix product operator, and show that the dissipation leads to a decay of operator entanglement, allowing us to capture the dynamics to long times. We benchmark this scheme by calculating spin and energy diffusion constants in a variety of physical models and compare to other existing methods.
Infraparticles are states that are not eigenstates of the mass operator. The considered infraparticle model is relevant for a recently constructed "string-localised" theory for QED which addresses the dressing of charged fields with so-called "photon clouds"; the non-perturbative dressing is described by vertex operators. I am particularly interested in the scattering of "free vertex states" which seems to exhibit a non-trivial exchange via a complex phase - similarly to a recently studied model in 2d (Dybalski, Mund). Vertex states are superselected with respect to the charge and the profile of the "photon clouds".
The interplay between disorder and interactions in quantum systems has recently attracted significant interest. An outstanding goal of current studies is to establish conditions for the existence of a phase of matter that violates ergodicity despite presence of interactions. Nevertheless, detecting convincing evidence of a phase transition between an ergodic and nonergodic phase the remains a challenging task. We will discuss two questions. The first is related to understanding why exact numerical studies can give rise to formulation of contradictory expectations of ergodicity breaking transitions for the same models. We show examples is which the behavior of physical quantities in a chain of interacting fermions with disorder is governed by the local integrals of motion of the Anderson insulator [1,2]. The second is related to the quest to establish toy models of ergodicity breaking transitions in quantum many-body systems. We will consider a model that is effectively zero dimensional and related to the model proposed by De Roeck and Huveneers to describe the avalanche mechanism of ergodicity breaking transition in one-dimensional disordered spin chains. We show that exact numerical results based on the spectral form factor calculation accurately agree with theoretical predictions, and hence unambiguously confirm existence of the ergodicity breaking transition in this model. We benchmark specific properties that represent hallmarks of the ergodicity breaking transition in finite systems [3].
[1] L. Vidmar, B. Krajewski, J. Bonča, and M. Mierzejewski, Phys. Rev. Lett. 127, 230603 (2021)
[2] B. Krajewski, L. Vidmar, J. Bonča, and M. Mierzejewski, arXiv:2209.00661
[3] J. Šuntajs and L. Vidmar, Phys. Rev. Lett. 129, 060602 (2022)
Ground state and thermal equilibrium properties of local quantum many-body systems can be explored with tensor networks, thanks to their area law entanglement. But highly excited states or out-of-equilibrium setups are much harder. These are therefore the natural problems in which quantum devices can potentially find the earliest advantage.
Energy filters allow us to access properties of the system at finite energy densities. They can be efficiently realized by quantum simulators or computers, which simulate the quantum dynamics, combined with classical filtering and sampling. But also replacing the quantum evolution by its classical simulation with tensor networks provides a new tool to classically compute dynamical properties of much larger systems than allowed by other methods.
In this talk I present the results of my masters thesis on
spontaneous baryogenesis. We determine the baryon asymmetry
of the universe numerically in a model of spontaneous baryogenesis.
Two different models are considered, a generic model of an
axion-like-particle and a model of a clockwork axion.
The clockwork model also generates a dark matter density.
Furthermore different couplings of the axion field to the standard
model are explored. Both models have been discussed in the literature
but the results have not been computed correctly.
We do this using a formalism, developed in the literature based on a
transport equation derived in linear response theory.
We apply this formalism to concrete models for the first time.
The Lindblad master equation is one of the main approaches to open quantum systems. While it has been widely applied in the context of condensed matter systems to study properties of steady states in the limit of long times, the actual route to such steady states has attracted less attention yet. Here, we investigate the nonequilibrium dynamics of spin chains with a local coupling to a single Lindblad bath and analyze the transport properties of the induced agnetization. Combining typicality and equilibration arguments with stochastic unraveling, we unveil for the case of weak driving that the dynamics in the open system can be constructed on the basis of correlation functions in the closed system, which establishes a connection between the Lindblad approach and linear response theory at finite times. This connection particularly implies that closed and open approaches
to quantum transport have to agree if applied appropriately. We demonstrate this fact numerically for the spin-1/2 XXZ chain at the isotropic point and in the easy-axis regime, where superdiffusive
and diffusive scaling is observed, respectively.
I will discuss the problem of unreasonable effectiveness of random matrix theory for description of spectral fluctuations in extended quantum lattice systems. A class oflocally interacting spin systems has been recently identified where the spectral form factor is proven to match with gaussian or circular ensembles of random matrix theory, and where spatiotemporal correlation functions of local observables as well as some measures of dynamical complexity can be calculated analytically. These, so-called dual unitary systems, include integrable, non-ergodic, ergodic, and generically, (maximally) chaotic cases. After reviewing the basic properties of dual unitary Floquet circuits, I will argue that correlation functions of these models are generally perturbatively stable with respect to breaking dual-unitarity, and describe a simple result within this framework.
Signatures of equilibrium phase transitions can be imprinted into the nonequilibrium dynamics of many-body quantum systems, resulting in the emergence of universal scaling laws out of equilibrium, as exemplified by the Kibble-Zurek mechanism. In a similar spirit, but novel setting, I report scaling and universality in open nonequilibrium quantum systems that are cooled towards a quantum critical point. The excess excitation density, which quantifies the degree of adiabaticity of the dynamics, is found to obey scaling laws in the cooling velocity as well as in the initial and final temperatures of the cooling protocol. The scaling laws are universal, governed by the critical exponents of the quantum phase transition. The validity of these statements is shown analytically for a Kitaev quantum wire coupled to Markovian baths, and subsequently argued to be valid under rather general conditions. Remarkably, these results establish that quantum critical properties can be probed dynamically at finite temperature, without even varying the control parameter of the quantum phase transitions.
Enhancing the light-matter coupling in cavities provides an intriguing route to control properties of matter, from chemical reactions to transport and thermodynamic phase transitions. Order parameters which couple linearly to the electromagnetic field, such as ferroelectricity, incommensurate charge density waves, or exciton condensates, appear most suitable in this context, but the possible mechanisms are not well understood in many cases. In this talk, I will discuss possibilities to manipulate interactions and band structures in a solid via the quantum fluctuations of the electromagnetic field; these results generalize the well-established Floquet engineering of correlated electrons to the regime of quantum light [1]. Specifically, this will be discussed for a model with competing superconductivity and charge density wave order [2]. Finally, we show how light-mediated interactions can be used to control ferroelectric order. We consider a minimal model of a two-dimensional material that couples to a surface plasmon polariton mode of a metal-dielectric interface. Within the mean-field approximation, the system exhibits a ferroelectric phase transition that is unaffected by the light-matter coupling. Bosonic dynamical mean-field theory provides a more accurate description and reveals that the photon-mediated interactions enhance the ferroelectric order and stabilize the ferroelectric phase [3].
[1] M. A. Sentef, J. Li, F. Künzel, and M. Eckstein, Phys. Rev. Research 2, 033033 (2020).
[2] J. Li and M. Eckstein, Phys. Rev. Lett. 125, 217402 (2020).
[3] K. Lenk, J. Li, Ph. Werner, M. Eckstein, Phys. Rev. B 106, 245124 (2022).
If anyone is unable to join the seminar in person, email me and we will stream it on
https://uni-goettingen.zoom.us/j/96249516311?pwd=Q2tURDFpcUVQaEQ3cXJSVk9wNkFPQT09
Manipulating quantum many-body states is a central milestone en route to harnessing quantum technologies. However, the exponential growth of the Hilbert space dimension with the number of qubits makes it challenging to classically simulate quantum many-body systems and consequently, to devise reliable and robust optimal control protocols. I will present a novel framework for efficiently controlling quantum many-body systems based on deep reinforcement learning (RL). Applications include the design of entangling two-body gates which outperform state-of-the-art pulse sequences used in superconducting qubits platforms, and the construction of circuit-based protocols to prepare ground states of quantum spin chains away from the adiabatic regime using ideas from counter-diabatic driving. To tackle the quantum many-body control problem, we leverage matrix product states (i) for representing the many-body state and, (ii) as part of the trainable machine learning architecture for our RL agent. In particular, we demonstrate that RL agents are capable of finding universal controls, of learning how to optimally steer previously unseen many-body states, and of adapting control protocols on-the-fly when the quantum dynamics is subject to stochastic perturbations.
