2025 Winter Semester

During the 2025 winter semester, the Quantum Information & Quantum Many-Body Physics seminar took place on Monday at 11:30 in the Erwin Schrödinger lecture hall (Boltzmanngasse 5, 5th floor). Occasionally, there were additional seminars out of schedule as announced here.

Shuhei Oyama (University of Vienna)

Higher Structures on Boundary Conformal Manifolds: Higher Berry Phase and Boundary Conformal Field Theory
Abstract: The space of conformal field theories, known as the conformal manifold, has a rich geometric structure. Locally, it is parametrized by exactly marginal operators, and its two-point functions endow it with a Riemannian metric. The existence of the conformal manifold places significant constraints on CFT data and plays an important role in string theory and holography. There are analogous spaces associated with boundary and defect exactly marginal deformations, known as the boundary and defect conformal manifolds. We discuss novel geometric structures—gerbe structures—on the boundary conformal manifold. Our approach is based on the notion of multi-wavefunction overlap, which was first proposed in the context of tensor networks to define a many-body generalization of the Berry phase, i.e., higher Berry phases. In this talk, I will first give a brief review of the formulation of the higher Berry phase in lattice systems. I will then focus on the similarity between tensor network states and boundary CFT states and use it to define a gerbe structure on the boundary conformal manifold. This talk is based on the preprint arXiv:2507.12525.

(date/time/location: 13.10.2025, 11:30, Erwin Schrödinger lecture hall, Boltzmanngasse 5, 5th floor)

Anna Francuz (University of Vienna)

Topological Order in the Rydberg Blockade on the Kagome Lattice with PEPS
Abstract: Topological order is notoriously difficult to detect—both theoretically and experimentally—due to the absence of local observables capable of distinguishing it from other long-range entangled phases. This challenge has motivated a shift from real materials toward quantum simulation platforms, particularly programmable Rydberg atom arrays, which offer promising avenues for realizing topological order. A notable example is the Kagome lattice quantum simulator demonstrated in Ref. [1]. In this work, we use two-dimensional Projected Entangled Pair States (PEPS) to variationally optimize the PXP model on the Kagome lattice. Our study also benchmarks a new algorithm for ground-state optimization with automatic differentiation (AD), as well as an algorithm for extracting F-symbols and modular data from topologically ordered PEPS. In my talk, I will introduce the concept of automatic differentiation and show the speedup achieved through implicit function differentiation, rather than direct differentiation of the fixed-point equations for both the VUMPS and symmetric CTM algorithms. Finally, I will present preliminary results from our PEPS optimization of the PXP model using the VUMPS contraction scheme.

[1] G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Samajdar, A. Omran, S. Sachdev, A. Vishwanath, M. Greiner, V. Vuletic, and M. D. Lukin,
Science 374, 1242 (2021).

(date/time/location: 20.10.2025, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Kevin Tam (University of Vienna)

Conformal Field Theory and Parton Approaches to SU(n)_k Chiral Spin Liquids
Abstract: Chiral spin liquids (CSLs) constitute bosonic analogues of the celebrated fractional quantum Hall states. Such examples of chiral topological order break time-reversal symmetry and exhibit gapless edge modes described by chiral conformal field theories (CFTs). In this seminar, I will first review some basic CFT [1]. I will then discuss some recent results from Liu et al. relating chiral correlators to parton states [2], two common approaches to constructing model wavefunctions for chiral systems.

[1] P. Di Francesco, P. Mathieu, and D. Sénéchal, Conformal Field Theory (1997).
[2] T. Liu, Y.-H. Wu, H.-H. Tu, and T. Xiang, “Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids,” Physical Review. B. (2025). doi.org/10.48550/arXiv.2501.09567

(date/time/location: 27.10.2025, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

David Blanik (University of Vienna)

Categorical gauging and emergent quantum double models
Abstract: It was recently observed [1] that iterated gauging of one-dimensional quantum many-body states invariant under the action of a finite abelian symmetry group yields ground states of abelian quantum double models. In this talk, I will give a pedagogical introduction to a recently proposed generalization [2] of the classic gauging procedure [3] to arbitrary fusion-categorical symmetries, and show that quantum double models also emerge in the non-abelian setting. This talk is based on ongoing work with José Garre-Rubio.

[1] Garre-Rubio. Emergent (2+1)D Topological Orders from Iterative (1+1)D Gauging. arXiv:2403.07575
[2] Vancraeynest-De Cuiper et al. From Gauging to Duality in One-Dimensional Quantum Lattice Models. arXiv: 2509.22051
[3] Haegeman et al. Gauging Quantum States: From Global to Local Symmetries in Many-Body Systems. arXiv:1407.1025

(date/time/location:03.11.2025, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

András Molnár (University of Vienna)

Exact Tensor Network eigenstates of local Hamiltonians
Abstract: In this talk I characterize exact tensor network (TN) eigenstates of local Hamiltonians. The characterization is a local equation involving the Hamiltonian terms and the tensors defining the TN state. We illustrate the statement for matrix product states (MPS). This equation has far-reaching applications such as finding an MPS path that satisfies the Schrödinger equation with a (time- dependent) local Hamiltonian path, characterizing exact scar states, or even characterizing exactly solvable models.

(date/time/location: 10.11.2025, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Paul Brehmer (University of Vienna)

Anatomy of a PEPS code
Abstract: In this seminar talk, I will explore the software modalities of modern tensor network numerics, with a focus on a growing ecosystem of open-source Julia packages initiated by colleagues in the Quantum Group at Ghent University [1, 2]. This suite of tools ranges from low-level tensor primitives to high-level algorithms, supporting performant and reproducible computational workflows in research. As a concrete case study, I will discuss the ongoing development of projected entangled-pair state (PEPS) algorithms [3], highlighting the challenges of managing complexity and ensuring interoperability in large-scale tensor network simulations.

[1] L. Devos and J. Haegeman, TensorKit.jl: A Julia package for large-scale tensor computations, with a hint of category theory, arXiv:2508.10076 (2025)
[2] QuantumKitHub, github.com/QuantumKitHub
[3] P. Brehmer, L. Burgelman, Z. Yue and L. Devos, PEPSKit.jl: A Julia package for projected entangled-pair state simulations (in preparation), https://github.com/QuantumKitHub/PEPSKit.jl

(date/time/location: 17.11.2025, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Refik Mansuroglu (University of Vienna)

Simulation Complexity of Gaussian Bosonic Hamiltonians
Abstract: The simulation of bosonic states under Gaussian Bosonic Hamiltonians can be very easy or very hard depending on whether squeezing is allowed or not. If squeezing is not allowed, certain moments of position and momentum observables can be efficiently simulated by a quantum computer. If it is allowed, the simulation becomes PostBQP-hard, meaning it would require arbitrary post-selection. I present a subclass of simulable Hamiltonians and prove hardness for the rest.

(date/time/location: 24.11.2025, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Andreas Klingler (University of Vienna)

Ground-State Degeneracy in 1D Frustration-Free Hamiltonians: Thresholds, Jumps, and Undecidability
Abstract: In this talk, I will discuss how the ground-state degeneracy of 1D frustration-free Hamiltonians with nearest-neighbor interactions behaves as the system size grows. The main question we explore is: if we know the ground-state degeneracy for small systems, what can we conclude about larger systems? I will first show that for commuting Hamiltonians, there is a clear threshold beyond which the degeneracy remains fixed. Moving to non-commuting Hamiltonians, we see that small-system behavior can be misleading, with degeneracy sometimes jumping unexpectedly at arbitrary size. Finally, we will see that in general, it is even undecidable to predict whether the degeneracy collapses or grows in the large-system limit.

(date/time/location: 01.12.2025, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Christian Reinmoser (University of Vienna)

Semidefinite Programming in Quantum Cryptographic Settings
Abstract: In this talk, I will discuss the basic usage of semidefinite programs in quantum cryptographic settings. As an initial example, I will introduce the problem of quantum coin-flipping and, based on [1], give a bound on the minimum bias of coin-flipping protocols. In a second part, I will follow the discussion in [2] about quantum strategies and quantum refereed games.

[1] A. Ambainis, H. Buhrman, Y. Dodis and H. Rohrig, "Multiparty quantum coin flipping," Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004., Amherst, MA, USA, 2004, pp. 250-259, doi.org/10.1109/CCC.2004.1313848.
[2] Gus Gutoski and John Watrous. 2007. Toward a general theory of quantum games. In Proceedings of the thirty-ninth annual ACM symposium on Theory of computing (STOC '07). Association for Computing Machinery, New York, NY, USA, 565–574. doi.org/10.1145/1250790.1250873

(date/time/location: 15.12.2025, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Mark Arildsen (University of Vienna)

Universal features of entanglement in (2+1)D chiral gapped states from the corners up
Abstract: (2+1)D chiral topological states that support a (1+1)D chiral conformal field theory (CFT) on the edge are expected to obey the Li-Haldane correspondence, which relates the low-lying levels of the spectrum of the entanglement Hamiltonian across a given bipartition to those of the spectrum of the Hamiltonian of the chiral edge CFT along the bipartition [1]. This picture works well for chiral gapped states in the topological regime of length scales, i.e., those well above the correlation length. In this talk, I will discuss Ref. [2]'s proposal for going beyond this regime. The authors of Ref. [2] hypothesize an operator generalization of the Li-Haldane correspondence, which they can use to understand the behavior of entanglement Hamiltonians of chiral gapped states in the presence of sharp corners. This is shown to yield universal features that characterize the "corner" regime of length scales, below the correlation length but still well above the lattice spacing, including a diagnostic of edge ungappability.

[1] Hui Li and F. D. M. Haldane, "Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States", Phys. Rev. Lett. 101, 010504 (2008). doi.org/10.1103/PhysRevLett.101.010504
[2] Xiang Li, Ting-Chun Lin, Yahya Alavirad, and John McGreevy, "Chiral gapped states are universally non-topological", arXiv:2510.23720. doi.org/10.48550/arXiv.2510.23720

(date/time/location: 12.01.2026, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Daniel Burgarth (FAU Erlangen-Nürnberg)

Error bounds for quantum dynamics with scale separation
Abstract: Many approximations in Quantum Physics rely on a separation of scale, such as the adiabatic theorem, Trotter dynamics, the Rotating Wave Approximation, the Zeno effect, to name a few. Over the last few years, our group has focused on developing error bounds for such approximations. Roughly speaking, the methodology can be split into three different mathematical scenarios: bounded energy scale, unbounded energy scale, and bounded but extensive scale, with the latter being relevant for many-body systems. This informal seminar collects some of the bounds we found and outlines the technical challenges mostly for the first two scenarios.

(date/time/location: 19.01.2026, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Ken Shiozaki (Yukawa Institute for Theoretical Physics, Kyoto University)

Higher Berry curvature and group action on parameter space in spin chain systems
Abstract: Our understanding of the geometric structures underlying the space of gapped quantum many-body states has been steadily advancing. In particular, one-dimensional gapped systems are known to support a three-form defined on the parameter space, which generalizes the conventional two-form Berry curvature familiar from quantum mechanics. 

In this talk, I will discuss how group actions on both the parameter space and the Hilbert space impose constraints on the global structure of invertible states, using the matrix product state representation. As an application of this framework, we demonstrate that the phase transition between the Haldane chain phase and the trivial phase acts as a source of the three-form higher Berry curvature.

Reference: Ken Shiozaki, "Equivariant Parameter Families of Spin Chains: A Discrete MPS Formulation", arXiv:2507.19932,  doi.org/10.48550/arXiv.2507.19932.

(date/time/location: 29.01.2026, 14:30, ESI (Erwin Schrödinger Institute), Schrödinger lecture hall, Boltzmanngasse 9, 1090 Vienna)

Ariel Kelman (HUJI)

Difficulties with Simulating Lattice Gauge Theories and the GGPEPS Method for Overcoming Them
Abstract: Lattice Gauge theories are a central computational tool in numerically studying Quantum Field Theory, the language of some of our most successful physical theories. Yet standard approaches run into a variety of challenges, such as (i) the exponential growth of computational resources required as a function of system size (endemic to all of quantum mechanics), (ii) the sign problem which arises when attempting to use probabilistic (generally Monte Carlo) methods using a probability distribution which is not guaranteed to be real-valued (in particular, may take on negative or complex values), and (iii) the inability to study time-evolution of physical systems that results from the standard Wick rotation involved in translating a quantum field theory into one that can be numerically simulated. In this talk, I will provide an overview of these challenges and discuss a particular tensor-network-based method that can address them, while avoiding particular difficulties with other tensor-network approaches, particularly relating to tensor contraction and the encoding of an entanglement area law. Recent results for a system suffering from the sign problem will be presented.

(date/time/location: 02.02.2026, 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)

Marta Florido Llinas (MPQ)

Generalizing the translationally invariant MPS framework
Abstract: In this talk I will present our recent work on developing a canonical form for uniform matrix product states (MPS) with a boundary matrix (https://www.arxiv.org/abs/2512.11968). The key ingredient is a structural characterization of arbitrary finite sets of matrices in terms of the algebra they generate and their span. Starting from the standard canonical description of uniform MPS with periodic boundary conditions, I will explain how to derive a generalized canonical form for MPS with boundaries, by extending the structural analysis of matrix sets to incorporate off-diagonal blocks and by introducing some notions inspired by formal language theory.

(date/time/location: 10.02.2026 11:30, Boltzmanngasse 5/Strudlhofgasse 4, 5th floor, Erwin Schrödinger lecture hall)