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.
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)
