We discuss a unified and systematic symmetry classification of general (interacting) open quantum systems coupled to a Markovian environment, described by a Lindbladian superoperator. Our classification is based on the behavior of the matrix representation of the Lindbladian under antiunitary symmetries and unitary involutions. We find that Hermiticity preservation reduces the number of symmetry classes, while trace preservation and complete positivity do not, and that the set of admissible
classes depends on the presence of additional unitary symmetries: in their absence or in symmetry sectors containing steady states, Lindbladians belong to one of ten non-Hermitian symmetry classes; if however, there are additional symmetries and we consider non-steady-state sectors, they belong to a different set of 14 classes. In both cases, it does not include classes with Kramer’s degeneracy. Moreover, we show that the examples in each class display unique random-matrix correlations. To fully resolve all symmetries, we employ the combined analysis of bulk complex spacing ratios and the overlap of eigenvector pairs related by symmetry operations. To conclude, we discuss how the classification can be extended to PT-symmetric fermionic Hamiltonians, by mapping the requirements of Hermiticity preservation and PT symmetry into each other. As a paradigmatic case study, we consider a two-site non-Hermitian Sachdev-Ye-Kitaev model. By varying the parameters of this model, we can realize 14 different classes in our classification.

*Lucas de Barros Pacheco Seara de Sá, Technical University of Lisbon

We develop a theory of measurement-induced phase transitions (MIPT) for d-dimensional lattice free fermions subject to random projective measurements of local site occupation numbers. Our analytical approach is based on the Keldysh path-integral formalism and replica trick.

In the limit of rare measurements, \gamma << J (where \gamma is measurement rate per site and J is hopping constant), we derive a non-linear sigma model (NLSM) as an effective field theory of the problem. Its replica-symmetric sector is a U(2)/U(1) x U(1) NLSM describing diffusive behavior of average density fluctuations. The replica-asymmetric sector, which describes propagation of quantum information in a system, is a (d+1)-dimensional isotropic NLSM defined on SU(R) manifold with the replica limit R->1, establishing close relation between MIPT and Anderson transitions. On the Gaussian level, valid in the limit \gamma/J -> 0, this model predicts “critical” (i.e. logarithmic enhancement of area law) behavior for the entanglement entropy.

However, one-loop renormalization group analysis shows [1] that for d=1, the logarithmic growth saturates at a finite value ~(J / \gamma)^2 even for rare measurements, implying existence of a single area-law phase. The crossover between logarithmic growth and saturation, however, happens at an exponentially large scale, ln(l_corr)∼J/\gamma, thus making it easy to confuse with a transition in a finite-size system.
Furthermore, utilizing \epsilon-expansion, we demonstrate [2] that the “critical” phase is stabilized for d > 1 with a transition to the area-law phase at a finite value of \gamma / J.

The analytical calculations are supported and are in excellent agreement with extensive numerical simulations [1,2] for d=1 and d=2. For d=2 we determine numerically the position of the transition and estimate the value of correlation length critical exponent.

[1] https://arxiv.org/abs/2304.03138
[2] https://arxiv.org/abs/2309.12405

Quantum Complexity has emerged in the past few years as a candidate for quantum chaos diagnostic. This talk is based on a work that appeared last year, in which we show that a notion of quantum complexity (spread complexity / Krylov state complexity) is sensitive to Topological Phase Transitions – at least for the prototypical Kitaev chain. I’ll give a brief overview of what we mean when we say “quantum” chaos, make connections with classical chaos and proceed to discuss our results by introducing the Krylov subspace methods.

*Nitin Gupta, University of Cape Town

The bulk-edge correspondence is a remarkable duality in condensed matter physics, relating the value of bulk topological invariants to the emergence of gapless edge modes. In the case of the integer quantum Hall effect, the value of the Hall conductivity is equal to the sum of signed edge modes, taking into account their chirality. For noninteracting systems, this fact is by now understood in full mathematical rigor. For interacting models, in the last years there has been progress in the rigorous understanding of bulk topological phases, but a lot less is known about interacting edge modes and about the bulk-edge duality. From the point of view of effective QFTs, the edge modes of 2d Hall systems are expected to be well described by the multichannel Luttinger model, a 1+1 dimensional integrable QFT. In this talk I will discuss how rigorous RG methods can be used to prove the emergence of the Luttinger liquid description from the 2d lattice model, and to control the deviations away from it at finite scales. The approach allows to exactly compute real-time edge transport coefficients, and in particular to prove the quantization of the edge conductance, thanks to the combination of lattice and emergent Ward identities. Joint work with Vieri Mastropietro.

*Marcello Porta, SISSA Trieste

Attention Unusual date, the seminar will take place on Friday

On 12th and 13th 2023 will be held the symposium on Nonequilibrium many-body dynamics in memory of our colleague and friend Marko Medenjak who passed away last year. All talks will be given in the F1 room on the ground floor of the Faculty of Physics building, Jadranska 19. The symposium is open to all interested. Please find the program here.

In talk I will show how to self-consistently couple the Einstein-inflaton equations to a strongly coupled quantum field theory (QFT) as described by holography. We show that this can lead to an inflating universe, a reheating phase and finally a universe dominated by the QFT in thermal equilibrium. Special attention will be given to technical details that could be of relevance for modelling of more general holographic set-ups that for instance include charge.

In quantum physics, topological properties usually emerge as a feature of equilibrium quantum states. We show that topological fingerprints can also manifest in the relaxation rates of open quantum systems. To demonstrate this we consider one of the simplest models that has two distinct topological phases in its ground state: the Kitaev model for the p-wave superconductor. After introducing dissipation to this model we estimate the Liouvillian gap in both strong and weak dissipative regimes. Our results show that a non-zero superconducting pairing opens a Liouvillian gap that remains open at large system sizes. At strong dissipation this gap is essentially unaffected by the topology of the underlying Hamiltonian ground state. In contrast, when dissipation is weak, the topological phase of the Hamiltonian ground state plays a crucial role in determining the character of the Liouvillian gap. We present the method used to extract this Liouvillian gap for a number of different dissipative processes.

I will discuss a semiclassical approach to form factors in the sinh-Gordon field theory in the background of a radial classical solution that describes a heavy exponential operator placed at the origin. I will introduce and study new special functions which generalize the Bessel functions and have a nice interpretation in the Tracy–Widom theory of the Fredholm determinant solutions of the classical sinh-Gordon model.

Unusual venue: F1 room, 1st floor

I will discuss the matrix quantum mechanics with potential corresponding to an arbitrary spectral curve. This can be seen as a generalization of the duality between JT gravity and a particular matrix integral. Using the recently developed techniques of quantum generalised hydrodynamics, the effective theory of the eigenvalue density fluctuations is a simple 2D free-boson BCFT on a curved background. The ensemble average over random matrices then corresponds to a quantum expectation value. Using this formalism we reproduce non-perturbative results for matrix integrals (the ramp and the plateau in the spectral form factor). We also compute the entanglement between eigenvalues,  matching a previous result by Hartnoll and Mazenc for the c = 1 matrix model and extending it to the general case. The hydrodynamical theory provides a clear picture of the emergence of spacetime in two dimensional string theory.

*Giuseppe Policastro, Laboratoire de Physique Théorique, ENS, Paris

New ! Before the seminar, you are invited to have pizzas in the seminar room at 12:45 (unusual venue, F1 classroom, Physics building first floor)