Obtaining quantitative predictions on whether, and under which conditions, a model or system enters a high-$T_c$ superconducting state is an ongoing and challenging endeavour. Here we present the Matrix-Product-State-plus-Mean-Field (MPS+MF) method, which allows to simulate multidimensional systems in and out of equilibrium in parameter regimes inaccessible to other methods (like QMC). We outline the general structure and capabilities of the method. We then demonstrate how to realize the analogue of a high-$T_c$ superconducting state in a t-J bi-plane lattice model with strongly enhanced inter-plane spin-spin coupling. These predictions have direct bearing for the ongoing, and so-far unfulfilled, quest to realize the analogues of high-$T_c$ superconducting states in experiments with ultra cold atomic gases, which can realize just these t-J biplane models.
Correlated quantum systems in 1D have a long and impactful history in the study of quantum matter. Many analytical and numerical insights that remain elusive for their higher-dimensional analogues are now available for these systems. Yet, the understanding that these isolated 1D models afford cannot directly be translated to equivalent ones in 2D and 3D. Quasi-1D systems, higher-dimensional systems comprised of many 1D sub-units weakly coupled to one another, offer a way out of this dilemma. This presentation will review our recent results, obtained with several collaborating groups, in using such systems to bootstrap the considerable power of methods originally developed for 1D to key challenges for higher-dimensional models in the domain of correlated quantum matter. Specifically, this talk will show how designing a high-Tc superconducting model material in 3D from microscopic first principles is possible using this approach [1,2], as is the study of induced superconductivity evolving out of non-equilibrium dynamics [3], or the gaining of new insight into Kivelson’s long-standing proposal for reservoir-enhanced superconductivity [4,5]. It will further be shown how quasi-1D systems are ideal proving grounds for powerful new hybrid algorithms to treat correlated quantum matter in 2D and 3D [6,7].
[1] Phys. Rev. X 13, 011039 (2023).
[2] Phys. Rev. B 111, 125141 (2025).
[3] SciPost Phys. 15, 236 (2023).
[4] arXiv:2507.18707 (accepted as Letter in PRB).
[5] arXiv:2602.11153 (in review at PRB)
[6] arXiv:2411.00480.
[7] Phys. Rev. B 112, 205133 (2025).
Rydberg tweezer arrays provide a versatile platform to explore quantum magnets. Different types of interactions, such as dipolar XY, van-der-Waals Ising ZZ, and spin-flip terms, can simultaneously exist. Furthermore, the Rydberg blockade mechanism can be used to prevent the excitation of another, nearby-situated Rydberg atom akin to the Gauss law in lattice gauge theory. In the talk I give an overview of the current state of the art and report on two different types of physics that can be realized with such platforms.
First, I comment on a recent experiment which exploited the blockade mechanism in order to observe the onset of a dynamically prepared, gapped Z2 quantum spin liquid on the ruby lattice (Semgehini et al, Science 374, 1242 (2021)). The thermodynamic properties of such models remain inadequately addressed, yet knowledge thereof is indispensable if one wants to prepare large, robust, and long-lived quantum spin liquids. Using large scale quantum Monte Carlo simulations we find a renormalized classical spin liquid which better explains part of the experimental observations than a quantum spin liquid. I comment on the adiabatic approximation to the dynamical ramps for the electric degrees of freedom, and the magnitude of the observed string parity order parameters. Second, through combining the dipolar XY and Ising ZZ interactions, we predict the existence of a robust supersolid phase on the triangular lattice for 100s of particles based on explicitly calculated pair interactions for 87Rb and with a critical entropy in reach of current technology. Such a lattice supersolid is long-lived, found over a wide parameter range in an isotropic and flat two-dimensional geometry. It has true long-range order, even at finite temperature, thanks to the dipolar interactions, and would constitute a rare example of the defect-induced paradigm of supersolidity.
Refs:
Phys.Rev. B 109, 144411 (2024)
Phys. Rev. A 111, L011305 (2025)
Phys. Rev. Lett. 134, 086601 (2025)
arXiv:2512.09040
Locally constrained gauge theories underpin our understanding of fundamental interactions in particle physics and the emergent behaviour of quantum materials. In strongly correlated systems, they can give rise to quantum spin liquids that lack conventional order and are defined by coherent superpositions of a large number of many-body configurations. Realising and probing such exotic states experimentally remains challenging due to the difficulty of enforcing local constraints and detecting the fragile coherences between many-body states. We report a large-scale (> 3,000 sites) realisation of a two-dimensional U(1) lattice gauge theory with ultracold atoms in a square optical superlattice and demonstrate non-equilibrium preparation of Rokhsar-Kivelson-like quantum spin liquid lakes within the constrained Hilbert space. We demonstrate Gauss’s law validity in a quench experiment, enabled by a new microscopy technique for detecting doubly occupied links. We observe characteristic real-space correlations and momentum-space pinch points, hallmarks of the emergent U(1) gauge structure in the prepared non-equilibrium quantum spin liquid lakes. Using round-trip interferometric protocols, we provide direct evidence for large-scale many-body coherence between the many-body configurations and probe the coherence length of the dynamically prepared quantum spin liquids. Our results establish non-equilibrium quantum simulation protocols as a powerful route for accessing and probing exotic, highly-entangled states beyond those hosted by the engineered Hamiltonian in thermal equilibrium.
Kontakt:
Prof. Dr. Heidrich-Meisner
Thu
30/04/26
Institute for Theoretical Physics/SR 3 A03.101
Theoretische Physik
14:15
Seminar Statistical Physics
Laila Henkes
ITP, Göttingen
Mean back relaxation as a quantifier for work in oscillatory systems
Many properties of quantum systems can be obtained from a single energy eigenstate. For example, its entanglement entropy can be used to identify ergodic behavior. Additionally, in ergodic systems, a single eigenstate also encodes thermal properties. During the presentation, we will demonstrate that local integrals of motion (LIOMs), which lie at the heart of integrability, can also be estimated from a small number of eigenstates. Their number decreases with system size, becoming a vanishing fraction of the Hilbert space dimension in the thermodynamic limit. As a result, a small number of eigenstates is also sufficient to establish thermal properties of integrable systems. Interestingly, this does not extend to LIOMs arising solely from Hilbert space fragmentation. This represents one of the few fundamental differences known between integrability and Hilbert space fragmentation.
The topic is motivated by the question of how eigenstates of many-body quantum systems change across the full many-body spectrum. I will consider *all* eigenstates of chaotic many-body quantum systems and of a class of random matrices chosen to mimic some behaviors of many-body Hamiltonians (power-law-banded random matrices). I will focus on the entropy of entanglement between two halves of the system, and describe the properties of eigenstate entanglement entropies in different parts of the spectrum.
Superconductivity and the fractional quantum Hall (FQH) effect are two landmark discoveries in modern physics. Superconductivity requires the presence of an effective pairing glue, which seems incompatible with the FQH effect, which requires strong repulsive interactions among electrons. Nevertheless, experiments in two-dimensional materials have recently observed both phases in close proximity to each other. A tantalizing explanation for this interplay is Laughlin's idea of “anyon superconductivity”, which proposes that superconductivity arises from a finite density of anyons — exotic quasiparticles emerging from the FQH state — carrying fractional charge. However, a key question is how Cooper pairing can occur in systems with purely repulsive interactions. I will demonstrate that anyon superconductivity can naturally emerge from an unconventional energy hierarchy of excitations when a missing ingredient is supplied: proximity to a topological phase transition. This provides a microscopic mechanism for anyon superconductivity, and allows us to construct the first controlled model for which low-energy Cooper pairs coexist with a FQH phase. I will present analytical and numerical results which could help guide future experiments and also allow us to describe continuous transitions between FQH states and chiral superconductors.
Understanding and simulating many-body quantum systems is an inherently challenging task. In
1981, Richard Feynman proposed that quantum systems could be effectively simulated by a
computer that follows the same principles as quantum mechanics. The idea of a quantum
computer was born. While many other applications for quantum computers have been
discovered since then, Feynman’s original idea, now called Digital Quantum Simulation (DQS),
has evolved from analog methods to advanced digital platforms, driven by significant
experimental progress, e.g., using ultracold atoms and trapped ions.
In this talk, I will provide an overview of the progression of DQS, from its initial concept to
current implementations [1]. Modern noisy quantum computers present challenges due to the
non-error-corrected nature of these systems. To navigate this landscape, novel quantum
algorithms, e.g. hybrid classical-quantum algorithms [2], have been developed to fit the
specifications of such devices. For DQS, the prevailing question today is: What problems are
amenable to be simulated on noisy quantum computers? I will discuss recent work on
simulating quantum many-body dynamics [3], algorithmic advances to describe ground state
phass [4,5] and the potential of stabilizing exotic non-equilibrium phases of matter,
e.g., discrete time crystals, using quantum-classical feedback [6].
Coexistence of different dynamical phases is a hallmark of glassy dynamics. This is well-studied in classical systems where the underlying theoretical framework is that of large deviation theory. The presence of a similar phase coexistence has been suggested in monitored quantum many-body systems, but the lack of suitable methods has yet prevented a systematic large deviation analysis. Here we present a tensor network framework that allows the application of large deviation theory to large quantum systems. Building on this, we locate a series of first-order dynamical phase transitions in a monitored discrete-time many-body quantum dynamics, at the level of the trajectory space. Crucially, our approach provides access not only to large-deviation statistics but also to conditioned quantum many-body states, enabling a microscopic characterization of the dynamical phases and their coexistence.
Kontakt:
Prof. Dr. Heidrich-Meisner
Thu
11/06/26
Institute for Theoretical Physics/SR 3 A03.101
Theoretische Physik
14:15
Seminar Statistical Physics
Gregor Häfner
ITP, Göttingen
Concurrently coupling particle and continuum simulations to study block copolymer membrane fabrication
Motivated by dynamical quantum phase transitions (DQPTs), we analyze the zeros of the survival amplitude: the times at which the overlap between an initial state and its time-evolved counterpart vanishes. Among all values that the survival amplitude can take, zeros play a distinguished role, and extending time to the complex plane reveals them beyond the real-time axis. Instead of tracking individual zeros, we focus on their coarse-grained distribution. We show that, on large scales, this distribution is controlled by the shape, or envelope, of the initial-state energy distribution. We illustrate this for various initial states in the Ising model with a tunable interaction range. For quenched BCS states in the nearest-neighbor limit, the envelope determines the exact positions of the zeros. In contrast, in the long-range limit, the zeros can first be described as following effective trajectories in the complex-time plane before reaching the positions predicted by the envelope. This envelope approach shows how changes in the initial state or in Hamiltonian parameters reshape the zero distribution via the corresponding deformation of the initial-state energy distribution.
Accurate numerical studies typically involve a diagonalization procedure that can only be applied to small quantum systems. Consequently, thermodynamic limit results for generic quantum systems are very rare. During the talk I will demonstrate that identifying local integrals of motion (LIOMs) belongs to this rare class of problems [1]. LIOMs are essential for the long-time dynamics and thermalization of closed quantum systems. We derive a method that provides exact LIOMs for Hamiltonian systems and also for arbitrarily large quantum circuits. When applied to (more realistic) nearly integrable models, it provides slow modes and approximate relaxation times. Our approach can be applied to problems that are very demanding for other numerical methods, and the codes [2] demonstrate its technical simplicity.
[1] J. Pawłowski, J. Herbrych, and M. Mierzejewski Phys. Rev. B 112, 155130 (2025).
[2] J Pawłowski, J Herbrych, M Mierzejewski, (https://github.com/JakubPawlowskii/InfiniteLIOMs) (2025)
I will show how basic aspects of the Riemannian geometry of the unitary group such as its curvature, tangent space and dense covering can guide the design of quantum algorithms. For this, we will derive an explicit formula for tangential gradients of linear cost functions which will show that corresponding state updates are in form of exponentials of commutators. Such unitary operations can be systematically implemented on quantum computers using the framework of double-bracket quantum algorithms which recently resulted in generalizations of the paradigmatic Grover's algorithm and new unitary synthesis formulas for implementing quantum signal processing. I will summarize the results of an ongoing collaboration developing this approach and I hope that at the end of the talk you will feel that knowing linear algebra is enough to take up designing quantum algorithms yourself.
