David J. Luitz, Ivan M. Khaymovich, Yevgeny Bar Lev

SciPost Phys. Core 2, 006 (2020) · published 30 April 2020 | Toggle abstract · pdf

The disordered XXZ model is a prototype model of the many-body localization transition (MBL). Despite numerous studies of this model, the available numerical evidence of multifractality of its eigenstates is not very conclusive due severe finite size effects. Moreover it is not clear if similarly to the case of single-particle physics, multifractal properties of the many-body eigenstates are related to anomalous transport, which is observed in this model. In this work, using a state-of-the-art, massively parallel, numerically exact method, we study systems of up to 24 spins and show that a large fraction of the delocalized phase flows towards ergodicity in the thermodynamic limit, while a region immediately preceding the MBL transition appears to be multifractal in this limit. We discuss the implication of our finding on the mechanism of subdiffusive transport.

Gianfranco Bertone, Djuna Croon, Mustafa A. Amin, Kimberly K. Boddy, Bradley J. Kavanagh, Katherine J. Mack, Priyamvada Natarajan, Toby Opferkuch, Katelin Schutz, Volodymyr Takhistov, Christoph Weniger, Tien-Tien Yu

SciPost Phys. Core 3, 007 (2020) · published 15 October 2020 | Toggle abstract · pdf

In this white paper, we discuss the prospects for characterizing and identifying dark matter using gravitational waves, covering a wide range of dark matter candidate types and signals. We argue that present and upcoming gravitational wave probes offer unprecedented opportunities for unraveling the nature of dark matter and we identify the most urgent challenges and open problems with the aim of encouraging a strong community effort at the interface between these two exciting fields of research.

Arpan Bhattacharyya, Wissam Chemissany, S. Shajidul Haque, Jeff Murugan, Bin Yan

SciPost Phys. Core 4, 002 (2021) · published 8 February 2021 | Toggle abstract · pdf

The harmonic oscillator is the paragon of physical models; conceptually and computationally simple, yet rich enough to teach us about physics on scales that span classical mechanics to quantum field theory. This multifaceted nature extends also to its inverted counterpart, in which the oscillator frequency is analytically continued to pure imaginary values. In this article we probe the inverted harmonic oscillator (IHO) with recently developed quantum chaos diagnostics such as the out-of-time-order correlator (OTOC) and the circuit complexity. In particular, we study the OTOC for the displacement operator of the IHO with and without a non-Gaussian cubic perturbation to explore genuine and quasi scrambling respectively. In addition, we compute the full quantum Lyapunov spectrum for the inverted oscillator, finding a paired structure among the Lyapunov exponents. We also use the Heisenberg group to compute the complexity for the time evolved displacement operator, which displays chaotic behaviour. Finally, we extended our analysis to N-inverted harmonic oscillators to study the behaviour of complexity at the different timescales encoded in dissipation, scrambling and asymptotic regimes.

Lenart Zadnik, Maurizio Fagotti

SciPost Phys. Core 4, 010 (2021) · published 29 April 2021 | Toggle abstract · pdf

We study an effective Hamiltonian generating time evolution of states on intermediate time scales in the strong-coupling limit of the spin-1/2 XXZ model. To leading order, it describes an integrable model with local interactions. We solve it completely by means of a coordinate Bethe Ansatz that manifestly breaks the translational symmetry. We demonstrate the existence of exponentially many jammed states and estimate their stability under the leading correction to the effective Hamiltonian. Some ground state properties of the model are discussed.

Shraddha Sharma, Xhek Turkeshi, Rosario Fazio, Marcello Dalmonte

SciPost Phys. Core 5, 023 (2022) · published 21 April 2022 | Toggle abstract · pdf

We explore the dynamical phases of unitary Clifford circuits with variable-range interactions, coupled to a monitoring environment. We investigate two classes of models, distinguished by the action of the unitary gates, which either are organized in clusters of finite-range two-body gates, or are pair-wise interactions randomly distributed throughout the system with a power-law distribution. We find the range of the interactions plays a key role in characterizing both phases and their measurement-induced transitions. For the cluster unitary gates we find a transition between a phase with volume-law scaling of the entanglement entropy and a phase with area-law entanglement entropy. Our results indicate that the universality class of the phase transition is compatible to that of short range hybrid Clifford circuits. Oppositely, in the case of power-law distributed gates, we find the universality class of the phase transition changes continuously with the parameter controlling the range of interactions. In particular, for intermediate values of the control parameter, we find a non-conformal critical line which separates a phase with volume-law scaling of the entanglement entropy from one with sub-extensive scaling. Within this region, we find the entanglement entropy and the logarithmic negativity present a cross-over from a phase with algebraic growth of entanglement with system size, and an area-law phase.