
chair: Johannes Richter

09:00  09:30

Annabelle Bohrdt
(Universität Regensburg & Harvard University)
How to find and probe pairs in doped quantum
A key step in unraveling the mysteries of materials exhibiting unconventional superconductivity is to understand the underlying pairing mechanism. While it is widely agreed upon that the pairing glue in many of these systems originates from antiferromagnetic spin correlations, a microscopic description of pairs of charge carriers remains lacking. In this talk, I will present stateofthe art numerical methods to probe the internal structure and dynamical properties of pairs of charge carriers in quantum antiferromagnets in fourlegged cylinders. Exploiting the full momentum resolution in our simulations, we are able to distinguish two qualitatively different types of bound states: a highly mobile, metastable pair, which has a dispersion proportional to the hole hopping t, and a heavy pair, which can only move due to spin exchange processes and turns into a flat band in the Ising limit of the model. We find qualitatively good agreement with the semianalytical geometric string theory. Based on the intuition gained with the geometric string theory, we introduce mixeddimensional models, which exhibit binding energies of the order of the spin exchange J and highly mobile pairs, and can be realized using cold atoms in optical lattices. We moreover relate the pair spectral function to the properties of FermiHubbard excitons and draw connections to the optical conductivity, thus enabling insights from and connections between theoretical models, quantum simulators, and solid state experiments.

09:30  10:00

Natalia Chepiga
(TU Delft)
Resilient infinite randomness criticality for a disordered chain of interacting Majorana fermions
The quantum critical properties of interacting fermions in the presence of disorder are still not fully understood. While it is well known that for Dirac fermions, interactions are irrelevant to the noninteracting infinite randomness fixed point, the problem remains largely open in the case of Majorana fermions which further display a much richer disorderfree phase diagram. Pushing the limits of DMRG simulations, we carefully examine the groundstate of a Majorana chain with both disorder and interactions. Building on appropriate boundary conditions and key observables such as entanglement, energy gap, and correlations, we strikingly find that the noninteracting Majorana IRFP is very stable against finite interactions, in contrast with previous claims.

10:00  10:30

Thomas Barthel
(Duke University)
Quantum simulation of condensed matter using Trotterized tensor networks
First, I will describe a variational quantum eigensolver for the simulation of stronglycorrelated quantum matter based on a multiscale entanglement renormalization ansatz (MERA) and gradientbased optimization. Due to its narrow causal cone, the algorithm can be implemented on noisy intermediatescale (NISQ) devices and still describe large systems. The number of required qubits is systemsize independent and increases only to a logarithmic scaling when using quantum amplitude estimation to speed up gradient evaluations. Translation invariance can be used to make computation costs squarelogarithmic in the system size and describe the thermodynamic limit. For the practical implementation, the MERA disentanglers and isometries are Trotterized, i.e., implemented as brickwall circuits. With a few Trotter steps, one recovers the accuracy of the full MERA. Results of benchmark simulations for various critical spin models establish a quantum advantage.
Secondly, I will address the question of barren plateaus in the optimization of isometric tensor network states. Barren plateaus correspond to scenarios where the average amplitude of the cost function gradient decreases exponentially with increasing system size. This occurs, for example, for quantum neural networks. We found that, in systems with finiterange interactions, variational optimization problems for matrix product states, tree tensor networks, and MERA are free of barren plateaus. The derived scaling properties of gradient amplitudes establish trainability and bear implications for efficient initialization procedures.
References:
arXiv:2108.13401  Q. Miao and T. Barthel, "A quantumclassical eigensolver using multiscale entanglement renormalization"
arXiv:2303.08910  Q. Miao and T. Barthel, "Convergence and quantum advantage of Trotterized MERA for stronglycorrelated systems"
arXiv:2304.00161  T. Barthel and Q. Miao, "Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network states"
arXiv:2304.14320  Q. Miao and T. Barthel, "Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus"

10:30  11:00

coffee break


chair: Andreas Honecker

11:00  11:30

Reinhard Noack
(PhilippsUniversität Marburg)
Finite PEPS and modetransformation DMRG methods for twodimensional Hubbard and related models
I discuss our work in applying tensornetwork methods to
twodimensional strongly correlated electron models. First, I discuss
our adaptation of the finiteprojectedentangledpairstate algorithm
(fPEPS) for the twodimensional Hubbard model. This adaptation uses
projected entangled pair operators (PEPOs), takes full advantage of
SU(2) symmetry, carries out both local variational optimization and
global gradientbased optimization of the PEPS, and implements a
number of other optimizations, so that we can treat lattice of up to
8x8 with PEPS bond dimension of up to 8. I discuss the accuracy and
performance of this algorithm and its effectiveness relative to other
methods. Second, I discuss work applying the DMRG with integrated mode
transformations to Hubbardlike models in general, applying it
spcefically to a twodimensional model of spinless fermions with
nearest and nextnearestneighbor hopping and nearestneighbor
Coulomb repulsion. I discuss the accuracy, computational cost and
performance of the method as well as the groundstate phase diagram of
the spinless fermion model at half filling.

11:30  12:00

Attila Szabó
(Max Planck Institute for the Physics of Complex Systems)
Highaccuracy variational Monte Carlo for frustrated magnets with deep neural networks
In this talk, I will show that neural quantum states based on very deep (416layered) neural networks can outperform stateoftheart variational approaches on highly frustrated quantum magnets. In particular, we use group convolutional neural networks (GCNNs), which allow us to impose all spacegroup symmetries and to target nontrivial symmetry sectors variationally. I will demonstrate the power of our method by obtaining stateoftheart ground and excitedstate energies for the $J_1J_2$ Heisenberg model on the square and the triangular lattices. I will also discuss GCNN studies of Heisenberg models on fullerene geometries, where we obtained the spectrum of lowlying excited states resolved by pointgroup symmetry. On larger fullerenes, these contain distinct “towers of states” akin to those expected in an ordered magnet: Indeed, we are able to reconstruct the corresponding “magnon operators” from the groundstate correlation functions, which show the gradual emergence of honeycomblike Néel order as the degree of frustration reduces.

12:00  12:30

Stefan Wessel
(RWTH Aachen)
Reduced basis surrogates of quantum manybody systems based on tensor networks
Within the reduced basis methods approach, an effective lowdimensional subspace of a quantum manybody Hilbert space is constructed in order to investigate, e.g., the groundstate phase diagram.
The basis of this subspace is built from solutions of snapshots, i.e., ground states corresponding to particular and wellchosen parameter values.
Here, we show how a greedy strategy to assemble the reduced basis and thus to select the parameter points can be implemented based on matrixproductstate (MPS) calculations.
Once the reduced basis has been obtained, observables required for the computation of phase diagrams can be computed with a computational complexity independent of the underlying Hilbert space for any parameter value.
We illustrate the efficiency and accuracy of this approach for different onedimensional quantum spin1 models, including anisotropic as well as biquadratic exchange interactions, leading to rich quantum phase diagrams.

12:30  13:30

lunch

13:30  14:00

discussion


chair: Matthias Vojta

14:00  14:30

Mathias Scheurer
(University of Stuttgart)
Exotic manybody physics in van der Waals moiré systems
When two layers of graphene are stacked on top of each other with a finite relative angle of rotation, a moiré pattern forms. Most strikingly, at socalled “magic angles”, the largest of which is around 1 degree, the bands around the Fermi surface flatten significantly; this enhances the density of states and the impact of electronelectron interactions. Soon after the experimental discovery in 2018 that this enhancement can induce superconductivity and other, including magnetic, instabilities, it became clear that twisted bilayer graphene is only one example of an engineered van der Waals moiré system with a complex phase diagram akin to other strongly correlated materials. In this talk, I will provide a brief introduction to the rich and diverse field of moiré superlattices built by stacking and twisting graphene and other van der Waals materials. I will further present recent and ongoing projects – involving a combination of analytics, numerics, machinelearning, and experiment – which explore the exotic quantum manybody phases that can be stabilized in these platforms.

14:30  15:00

Gaurav Chaudhary
(University of Cambridge)
Flat bands and correlations in twisted multilayers of topological insulators
Twisted bilayer graphene (TBG) near the "magic angles" has emerged as a rich platform for strongly correlated states of twodimensional (2D) Dirac semimetals.
Topological insulator thin films because of their ability to host low energy Dirac nodes, presents another platform where "twistronics" can be used to engineer flat bands. However, topological insulator systems encounter some theoretical difficulties in engineering flat bands using the twistronics approach. I will discuss these issues. Using simple surface state electronic models for thin film magnetic topological insulators, I will show how flat moire bands can still be achieved in these systems. I will discuss the similarity and differences of such moire systems with the twisted multilayers of graphene and more recent developments in twisted multilayers of cuprate superconductors. Finally, I will discuss possible many body phases that can appear in these moire systems.

15:00  15:30

Wonjune Choi
(Technical University of Munich)
Finite temperature entanglement negativity of fermionic topological phases and quantum critical points
We study the logarithmic entanglement negativity of symmetryprotected topological phases (SPTs) and quantum critical points (QCPs) of onedimensional noninteracting fermions at finite temperatures. In particular, we consider a free fermion model which realizes not only quantum phase transitions between gapped topological phases but also an exotic topological phase transition between quantum critical states, namely the fermionic Lifshitz transition. We show that the bipartite entanglement negativity between two adjacent blocks of fermions sharply reveals the crossover boundary of the quantum critical fan near the QCP between the gapped phases. Along the critical phase boundary between the gapped phases, the sudden decrease in the entanglement negativity signals the fermionic Lifshitz transition responsible for the change in the topological nature of the QCPs. The hightemperature series expansion of the density operator shows that the entanglement negativity of every gapped and gapless state is converged to zero as $\sim T^{2}$ in the hightemperature limit. We further demonstrate that the tripartite entanglement negativity between two spatially separated disjoint blocks of fermions can count the number of topologically protected boundary modes for both SPTs and topologically nontrivial QCPs at zero temperature. The longdistance entanglement between the boundary modes vanishes at finite temperatures due to the instability of SPTs protected by onsite symmetries.

15:30  16:00

coffee break


chair: Sonia Haddad

16:00  16:30

Lucile Savary
(CNRS, École Normale Supérieure de Lyon)
Thermal Hall transport from phonons in quantum materials
I will present several approaches to the study of thermal Hall transport in quantum materials (esp. quantum magnets) when the main thermal Hall contribution is due to the transport of phonons coupled with electronic degrees of freedom.

16:30  17:00

Urban Seifert
(University of California, Santa Barbara)
MoiréMott insulators in transition metal dichalcogenides: Spin liquids and doping
Moiré heterostructures of transition metal dichalcogenides (TMD) have been shown to give rise to correlated insulating states at fractional fillings, forming selforganized charge lattices. The combination of spinorbit coupling and moiré modulation can lead pseudomagnetic fields and associated fluxes patterns for electrons. We explore the possibility of spinliquid states in these systems. We further discuss the effects of doping these correlated insulating states at fractional fillings.

17:00  17:30

Robin Schäfer
(Boston University)
Abundance of hardhexagon crystals in the quantum pyrochlore antiferromagnet
We present a novel proposal for potential ground states of the $S=1/2$ and $S=1$ Heisenberg antiferromagnet on the pyrochlore lattice. The groundstate candidates form a simple family that is exponentially numerous in the linear size of the system. They can be visualized as coverings of hard hexagons, with each hexagon representing a resonating valencebond ring, breaking various lattice symmetries such as rotation, inversion, and translation.
By evaluating a simple variational wavefunction based on a single hardhexagon covering, we achieve a precise variational energy consistent with density matrix renormalization group predictions and a numerical linked cluster expansion technique carried out at zero temperature. The scenario of a hardhexagon state is backed up by carefully examining excitations on top of the valencebond crystal as it provides further evidence of its stability.
Our findings have broader implications as they extend to other frustrated magnets, such as the twodimensional ruby and checkerboard lattices. In total, our work offers a new perspective, where the frustration effectively decouples unfrustrated motifs  the hard hexagons in the pyrochlore lattice  in quantum magnets.
[1] Robin Schäfer, Benedikt Placke, Owen Benton, Roderich Moessner, arXiv:2210.07235

17:30  18:30

informal discussion with senior scientists

18:30  19:30

dinner
