The ability to prepare a physical system in a desired quantum state is central to many areas of physics such as nuclear magnetic resonance, cold atoms, and quantum computing. Preparing states quickly and with high fidelity remains a formidable challenge. In this work we implement cutting-edge Reinforcement Learning (RL) techniques to find short, high-fidelity driving protocols from an initial to a target state in non-integrable single-particle and many-body quantum spin systems. The quantum state preparation problem, viewed as an optimization problem, is shown to exhibit examples of prototypical equilibrium phase transitions in classical macroscopic systems: both first and second order phase transitions, a glass phase, and symmetry breaking, as a function of the protocol duration. These control phase transitions, present even in low-dimensional clean quantum systems, are classical yet of non-equilibrium nature, and carry far-reaching consequences for manipulating quantum states.

******Marin Bukov,*** ***Department of Physics, Boston University*

A transformation that accounts for the universality found in Ref. [1] concerning the finite energy behavior of dynamical correlation functions of both integrable and non-integrable 1D correlated systems is used to generate from the pseudo-fermion dynamical theory of the integrable 1D Hubbard model [2] a corresponding renormalized theory with additional electron finite-range interactions [3,4]. The obtained renormalized theory is used to describe the experimental spectral lines in the angle resolved photoemission spectroscopy of the 1D quantum line defects in the 2D van der Waals layered semiconductor MoSe2 [3] and of the quasi-1D compound TTF-TCNQ [4]. The theoretical predictions refer to finite-energy ω windows in the vicinity of the cusps of the observed spectral lines. The dispersions and (k, ω)-plane weight distributions of such two systems are found to exactly follow those predicted by the non-integrable finite-range renormalized model with the exponent α for the density of states suppression, |ω| α, being given by α ≈ 0.73 − 0.78 for the MoSe2 line defects [3] and α ≈ 0.53 for TTF-TCNQ [4]. The latter value is thirteen times larger than that predicted by the simple 1D Hubbard model, α ≈ 0.04, for which α ∈ [0, 1/8] [5].

[1] A. Imambekov and L. I. Glazman Science 323 228 (2009).

[2] J. M. P. Carmelo and T. Cadez Nuclear Physics B 914, 461 (2017).

[3] Y. Ma, H. C. Diaz, J. Avila, C. Chen, V. Kalappattil, R. Das, M.-H. Phan, T. Cadez, J. M. P. Carmelo, M. C. Asensio, and M. Batzill Nature Communications 8, 14231 (2017).

[4] J. M. P. Carmelo, T. Cadez, M. Sing, and R. Claessen (Work in progress).

[5] M. Sing, U. Schwingenschlogl, R. Claessen, P. Blaha, J. M. P. Carmelo, L. M. Martelo, P. D. Sacramento, M. Dressel, and C. S. Jacobsen, Physical Review B 68 125111 (2003) .

***** *J. M. P. Carmelo, Universidade do Minho, Portugal*

I will first introduce formation probability as a quantity which can determine the universality class of a quantum critical system. In other words, by calculating this quantity one can find the central charge and critical exponents of a quantum system and determine the universality class uniquely. I will show that calculating this quantity boils down to finding Casimir energy of two needles. Then using boundary conformal field theory (BCFT) techniques we find exact results for the formation probabilities. Numerical results for transverse field Ising model will be presented to support the analytical results. Then we will briefly talk about Shannon mutual information as another quantity which can play similar role. We will present a conjecture which connects Shannon mutual information to the central charge of the underlying conformal field theory. We will support the conjecture with many numerical calculations. Finally, we will introduce post-measurement entanglement entropy as a tripartite measure of entanglement. We will show that this quantity is related to the Casimir energy of needles on Riemann surfaces and can be calculated exactly for conformal field theories. To do that we use a slightly different method than twist operator technique. Many analytical results, such as, Renyi entropy, entanglement Hamiltonian, distribution of the eigenvalues of entanglement Hamiltonian, the effect of the boundary and Affleck-Ludwig boundary entropy can be discussed naturally in our framework. Few numerical results regarding free bosons and transverse field Ising chain will be presented as support for analytical results.

***** *Mohammad Ali Rajabpour, Instituto de Fisica Universidade Federal Fluminense Niteroi, Rio de Janeiro*

We developed a novel perturbative expansion for the effective Hamiltonian governing the dynamics of periodically kicked systems in the small parameter of the kick strength. The expansion is based on the replica trick, and is formally equivalent to the infinite resummation of the Baker-Campbell-Hausdorff series in the non-kicked Hamiltonian, while taking finite order terms in the kicks. As an application of the replica expansion, we study the heating properties of a periodically kicked spin chain. We demonstrate that even away from the high frequency driving limit, the heating rate is at least stretched exponentially suppressed in the kick strength. This leads to a long pre-thermal regime, where the dynamics is governed by the effective Hamiltonian obtained from the expansion.

***** *Szabolcs Vajna, Faculty of Mathematics and Physics, University of Ljubljana*

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