arXiv subjects

Giuliano Giudici

Publications and source records attributed to Giuliano Giudici.

22 records · Page 2Linked to original sources

arXiv2019

Breakdown of ergodicity in disordered U(1) lattice gauge theories

We show how U(1) lattice gauge theories display key signatures of ergodicity breaking in the presence of a random charge background. Contrary to the widely studied case of spin models, in the presence of Coulomb interactions, the spectral properties of such lattice gauge theories are very weakly affected by finite-volume effects. This allows to draw a sharp boundary for the ergodic regime, and thus the breakdown of quantum chaos for sufficiently strong gauge couplings, at the system sizes accessible via exact diagonalization. Our conclusions are independent on the value of a background topological angle, and are contrasted with a gauge theory with truncated Hilbert space, where instead we observe very strong finite-volume effects akin to those observed in spin chains.

cond-mat.str-el↗

arXiv2019

Lattice gauge theories and string dynamics in Rydberg atom quantum simulators

Gauge theories are the cornerstone of our understanding of fundamental interactions among particles. Their properties are often probed in dynamical experiments, such as those performed at ion colliders and high-intensity laser facilities. Describing the evolution of these strongly coupled systems is a formidable challenge for classical computers, and represents one of the key open quests for quantum simulation approaches to particle physics phenomena. Here, we show how recent experiments done on Rydberg atom chains naturally realize the real-time dynamics of a lattice gauge theory at system sizes at the boundary of classical computational methods. We prove that the constrained Hamiltonian dynamics induced by strong Rydberg interactions maps exactly onto the one of a $U(1)$ lattice gauge theory. Building on this correspondence, we show that the recently observed anomalously slow dynamics corresponds to a string-inversion mechanism, reminiscent of the string-breaking typically observed in gauge theories. This underlies the generality of this slow dynamics, which we illustrate in the context of one-dimensional quantum electrodynamics on the lattice. Within the same platform, we propose a set of experiments that generically show long-lived oscillations, including the evolution of particle-antiparticle pairs. Our work shows that the state of the art for quantum simulation of lattice gauge theories is at 51 qubits, and connects the recently observed slow dynamics in atomic systems to archetypal phenomena in particle physics

cond-mat.quant-gas↗

arXiv2019

Diagnosing Potts criticality and two-stage melting in one-dimensional hard-boson models

We investigate a model of hard-core bosons with infinitely repulsive nearest- and next-nearest-neighbor interactions in one dimension, introduced by Fendley, Sengupta and Sachdev in Phys. Rev. B 69, 075106 (2004). Using a combination of exact diagonalization, tensor network, and quantum Monte Carlo simulations, we show how an intermediate incommensurate phase separates a crystalline and a disordered phase. We base our analysis on a variety of diagnostics, including entanglement measures, fidelity susceptibility, correlation functions, and spectral properties. According to theoretical expectations, the disordered-to-incommensurate-phase transition point is compatible with Berezinskii-Kosterlitz-Thouless universal behaviour. The second transition is instead non-relativistic, with dynamical critical exponent $z > 1$. For the sake of comparison, we illustrate how some of the techniques applied here work at the Potts critical point present in the phase diagram of the model for finite next-nearest-neighbor repulsion. This latter application also allows to quantitatively estimate which system sizes are needed to match the conformal field theory spectra with experiments performing level spectroscopy.

cond-mat.quant-gas↗

arXiv2017

The Coprime Quantum Chain

In this paper we introduce and study the coprime quantum chain, i.e. a strongly correlated quantum system defined in terms of the integer eigenvalues $n_i$ of the occupation number operators at each site of a chain of length $M$. The $n_i$'s take value in the interval $[2,q]$ and may be regarded as $S_z$ eigenvalues in the spin representation $j = (q-2)/2$. The distinctive interaction of the model is based on the coprimality matrix $\bf Φ$: for the ferromagnetic case, this matrix assigns lower energy to configurations where occupation numbers $n_i$ and $n_{i+1}$ of neighbouring sites share a common divisor, while for the anti-ferromagnetic case it assigns lower energy to configurations where $n_i$ and $n_{i+1}$ are coprime. The coprime chain, both in the ferro and anti-ferromagnetic cases, may present an exponential number of ground states whose values can be exactly computed by means of graph theoretical tools. In the ferromagnetic case there are generally also frustration phenomena. A fine tuning of local operators may lift the exponential ground state degeneracy and, according to which operators are switched on, the system may be driven into different classes of universality, among which the Ising or Potts universality class. The paper also contains an appendix by Don Zagier on the exact eigenvalues and eigenvectors of the coprimality matrix in the limit $q \rightarrow \infty$.

cond-mat.str-el↗