I will present our on-going work on quantum time evolution after a local quench at an interface between paramagnetic and ferromagnetic regions of a transverse field Isingmodel. The two regions are related by the Kramers-Wannier duality and thus support elementary excitations with the same energy dispersion but different physical nature. For open chain geometry a novel symmetry appears, a combination of the Kramers-Wannier transformation and a reflection, which squares to the Ising Z_2 symmetry. I will also present our first numerical results of time evolution at the interface.

Large-N quantum field theories are a playground for doing non-perturbative physics. Certain large-N theories turn out to be asymptotically free in d=4 and have features like bound states, just like quantum chromodynamics (QCD) and Yang–Mills theories. Their asymptotic freedom is connected to their apparent non-Hermiticity. However, when coupled with an antilinear symmetry, in many cases referred to as PT symmetry, this non-Hermicity does not prevent such theories from having real, bounded spectra and a notion of unitarity. It’s possible to calculate equations of state, phase diagrams, and transport coefficients like shear viscosity η/s in these theories. I will talk in particular about the O(N) model, which is relevant to Higgs physics when N=4. I’ll discuss the phase structure at large N. There is a first-order phase transition at finite temperature, which has implications for cosmology. In particular, the stable vacuum is not the spontaneous symmetry broken (SSB) vacuum, as is otherwise assumed in the Standard Model of particle physics. I’ll demonstrate how one can generate “mass from nothing”, without SSB, when a massless Higgs field is coupled to a U(1) Abelian gauge field. Lastly, I’ll briefly talk about how large-N techniques in the O(N) model are analogous to a method for non-perturbative analytical calculations in QCD and Yang–Mills theories, via so-called Rn resummation methods. This analogy might allow a study of the phase structure, transport coefficients, and confinement in QCD and Yang–Mills, with applications to the quark–gluon plasma and neutron stars.

We introduce a spin-chain model with dynamics consisting of a unitary circuit with discrete conformal symmetry. This model is holographically dual to a toy theory of quantum gravity in 2+1 dimensions, where certain tensor-network states correspond to classical discrete geometries. Unlike previous approaches, like holographic codes, these tensor networks and geometries evolve in time, reproducing some phenomena from general relativity. Also, these states satisfy the Ryu-Takayanagi correspondence between entanglement and geometry, but they provide much more, they contain a complete description of the bulk, including the interior of black holes, a feature that is not so transparent in standard AdS/CFT.

I will discuss the kinetic Boltzmann equation in the relaxation time approximation (RTA), a simple way to analytically obtain information of collective real-time transport. I will present the analytically computed retarded two-point Green’s functions of conserved operators in thermal states at non-zero density, and in the absence/presence of broken translational symmetry. This naturally leads to a discussion of the analytic structure and the transport properties such correlators imply. Looking forward, I will go beyond the usual standard truncation scheme used to close the BBGKY heirarchy and how such modifications lead to novel complex structure.

We show how functional relations, which can be considered as a definition of a quantum integrable theory, entail an integral equation that can be extended upon introducing dynamical variables to a Marchenko-like equation. Then, we naturally derive from the latter a classical Lax pair problem. We exemplify our method by focusing on the massive/massless version of the ODE/IM (Ordinary Differential Equations/Integrable Models) correspondence involving the sinh-Gordon/Lioville model, first emerged in the gauge theories and scattering amplitudes/Wilson loops AdS3 context with many moduli/masses, but in a way which reveals its generality. In fact, we give some hints, in the end, to its application to spin chains.

All lectures will take place in the seminar room 133 (Jadranska Ulica 21, new building). The schedule is

Please find the program of the 11th Trieste-Ljubljana-Zagreb meeting

Simulation of the single-particle tunneling problem by means of the Suzuki-Trotter approximation (STA) is analyzed. The target system describes a particle hopping across a chain of sites with position-dependent potential profile. The latter is assumed to be smooth and posses several local minima separated by a potential barrier, arranging a tunneling problem between the localized states in different minima. The STA error is found to manifest itself in three ways: i) perturbative energy shifts, ii) nonperturbartive renormalization of the tunneling rates, and iii) perturbative leakage of total probability to other states. In the general case, the first type of error is the most essential, as the emerging detuning of the tunneling resonance has to be compared with exponentially small tunneling rates. In absence of detuning (e.g. if the resonance is protected by symmetry), STA is found to cause exponential enhancement of the tunneling rates. The last type of error classifies the overall defect in the wave function and thus delineates the region of sufficiently weak distortion of the wave function due to STA. The conducted analysis confirms the naive criteria of applicability max{T, P } ≪ 1/δt (with T, P being the typical scales of kinetic and potential terms, respectively), while also revealing the structure of error and its actual behavior with system parameters. Analysis of the case of large Trotter step is also performed, with the main result being the reconstruction of the low-energy spectrum due to coupling between states with energy difference close to 2π/δt. The connection of the obtained results with the rigorous upper error bounds on the STA error is discussed, with particular emphasis on the reasons for the fact that these rigorous bounds are not always saturated. We also point out that the proposed problem can be directly implemented on existing quantum devices [arXiv:2012.00921]. In particular, we give a detailed description of an experimental design that demonstrates the described physics. The talk is based on the recent paper [arXiv:2312.04735].

We study the out-of-time-order correlation function (OTOC) in a
lattice extension of the Sachdev-Ye-Kitaev (SYK) model with quadratic
perturbations. The results obtained are valid for arbitrary time
scales, both shorter and longer than the Ehrenfest time. We
demonstrate that the region of well-developed chaos is separated from
the weakly chaotic region by the “front region”, which moves
ballistically across the lattice. The front velocity is calculated for
various system’s parameters, for the first time for SYK-like models.

*Aleksey Lunkin, Landau Institute Moscow*