Quantum and Topological Matter meeting
Speakers: Maksym Serbyn (Vienna), Rodrigo Arouca (UU) and Yaroslav Herasimenko (Leiden). Location: Amsterdam.
14:30 - 15:00 Welcome coffee and tea
15:00 - 15:45 Maksym Serbyn (Vienna) - Variational perspective on quantum many-body scars
15:45 - 16:30 Rodrigo Arouca (UU) - Thermodynamics of higher-order topological insulators
16:30 - 16:45 Coffee, Tea
16:45 - 17:30 Yaroslav Herasimenko (Leiden) - A diagrammatic approach to variational quantum ansatz construction
17:30 - 18:30 Drinks and snacks
Maksym Serbyn (Vienna)
Variational perspective on quantum many-body scars
The statistical mechanics description of many-particle systems rests on the assumption of ergodicity, the ability of a system to explore all allowed configurations in the phase space. For quantum many-body systems, statistical mechanics predicts the equilibration of highly excited non-equilibrium state towards a featureless thermal state. Hence, it is highly desirable to explore possible ways to avoid ergodicity in quantum systems. Many-body localization presents one generic mechanism for a strong violation of ergodicity relying on the presence of quenched disorder. In my talk I will discuss a different mechanism of the weak ergodicity breaking relevant for the experimentally realized Rydberg-atom quantum simulator . I will concentrate on the variational description of unusual quantum many-body revivals that originate from the special eigenstates. I will relate this dynamics to presence of stable periodic trajectories within time-dependent variational principle (TDVP) description of dynamics . I will use TDVP to find new “scars” and explore their response to perturbations of the Hamiltonian in one and two spatial dimensions for different lattice geometries. For two dimensional systems I will introduce the synchronization mechanism that helps stabilizing quantum revivals and mitigates boundary effects . Finally, I will discuss a new opportunities for the creation of novel states with long-lived coherence in systems that are now experimentally realizable .
 Probing many-body dynamics on a 51-atom quantum simulator, H. Bernien, et al., Nature 551, 579–584 (2017), arXiv:1707.04344
 Slow quantum thermalization and many-body revivals from mixed phase space, A. A. Michailidis, C. J. Turner, Z. Papić, D. A. Abanin, M. Serbyn, arXiv:1905.08564
 A. A. Michailidis, C. J. Turner, Z. Papić, D. A. Abanin, M. Serbyn, in preparation
Rodrigo Arouca (UU)
Thermodynamics of higher-order topological insulators
Abstract: We investigate the order of the topological quantum phase transition in a two dimensional quadrupolar topological insulator within a thermodynamic approach. Using numerical methods, we separate the bulk, edge and corner contributions to the grand potential and detect different phase transitions in the topological phase diagram. The transitions from the quadrupolar to the trivial or to the dipolar phases are well captured by the thermodynamic potential. On the other hand, we have to resort to a grand potential based on the Wannier bands to describe the transition from the trivial to the dipolar phase. The critical exponents and the order of the phase transitions are determined and discussed in the light of the Josephson hyperscaling relation.
Ref: Thermodynamics of a Higher-Order Topological Insulator, R. Arouca, S. N. Kempkes, C. Morais Smith, arXiv:1912.09159
Yaroslav Herasimenko (Leiden)
A diagrammatic approach to variational quantum ansatz construction
Abstract: Variational quantum eigensolvers (VQEs) are a promising class of quantum algorithms for preparing approximate ground states in near-term quantum devices. Minimizing the error in such an approximation requires designing ansatzes using physical considerations that target the studied system. One such consideration is size-extensivity, meaning that the ground state quantum correlations are to be compactly represented in the ansatz. On digital quantum computers, however, the size-extensive ansatzes usually require expansion via Trotter-Suzuki methods. These introduce additional costs and errors to the approximation. In this work, we present a diagrammatic scheme for the digital VQE ansatzes, which is size-extensive but does not rely on Trotterization. We start by designing a family of digital ansatzes that explore the entire Hilbert space with the minimum number of free parameters. We then demonstrate how one may compress an arbitrary digital ansatz, by enforcing symmetry constraints of the target system, or by using them as parent ansatzes for a hierarchy of increasingly long but increasingly accurate sub-ansatzes. We apply a perturbative analysis and develop a diagrammatic formalism that ensures the size-extensivity of generated hierarchies. We test our methods on a short spin chain, finding good convergence to the ground state in the paramagnetic and the ferromagnetic phase of the transverse-field Ising model.
Room C4.174, Science Park 904, University of Amsterdam.
Vladimir Gritsev, v.gritsev [at] uva [dot] nl
This event is part of a regular series of meetings on Quantum and Topological Matter, sponsored by Delta ITP, with the objective of bringing together the theoretical physics communities in Amsterdam, Leiden, Utrecht.