Publications

Order by: publication date number of citations

• On computing non-equilibrium dynamics following a quench

  Neil J. Robinson, Albertus J. J. M. de Klerk, Jean-Sébastien Caux

  SciPost Phys. 11, 104 (2021) · published 9 December 2021 | Toggle abstract · pdf

  Computing the non-equilibrium dynamics that follows a quantum quench is difficult, even in exactly solvable models. Results are often predicated on the ability to compute overlaps between the initial state and eigenstates of the Hamiltonian that governs time evolution. Except for a handful of known cases, it is generically not possible to find these overlaps analytically. Here we develop a numerical approach to preferentially generate the states with high overlaps for a quantum quench starting from the ground state or an excited state of an initial Hamiltonian. We use these preferentially generated states, in combination with a "high overlap states truncation scheme" and a modification of the numerical renormalization group, to compute non-equilibrium dynamics following a quench in the Lieb-Liniger model. The method is non-perturbative, works for reasonable numbers of particles, and applies to both continuum and lattice systems. It can also be easily extended to more complicated scenarios, including those with integrability breaking.

  5 citations

• Dual applications of Chebyshev polynomials method: Efficiently finding thousands of central eigenvalues for many-spin systems

  Haoyu Guan, Wenxian Zhang

  SciPost Phys. 11, 103 (2021) · published 8 December 2021 | Toggle abstract · pdf

  Computation of a large group of interior eigenvalues at the middle spectrum is an important problem for quantum many-body systems, where the level statistics provides characteristic signatures of quantum chaos. We propose an exact numerical method, dual applications of Chebyshev polynomials (DACP), to simultaneously find thousands of central eigenvalues, where the level space decreases exponentially with the system size. To disentangle the near-degenerate problem, we employ twice the Chebyshev polynomials, to construct an exponential semicircle filter as a preconditioning step and to generate a large set of proper basis states in the desired subspace. Numerical calculations on Ising spin chain and spin glass shards confirm the correctness and efficiency of DACP. As numerical results demonstrate, DACP is $30$ times faster than the state-of-the-art shift-invert method for the Ising spin chain while $8$ times faster for the spin glass shards. In contrast to the shift-invert method, the computation time of DACP is only weakly influenced by the required number of eigenvalues, which renders it a powerful tool for large scale eigenvalues computations. Moreover, the consumed memory also remains a small constant (5.6 GB) for spin-$1/2$ systems consisting of up to $20$ spins, making it desirable for parallel computing.

  1 citation

• Rotating 5D black holes: Interactions and deformations near extremality

  Alejandra Castro, Juan F. Pedraza, Chiara Toldo, Evita Verheijden

  SciPost Phys. 11, 102 (2021) · published 7 December 2021 | Toggle abstract · pdf

  We study a two-dimensional theory of gravity coupled to matter that is relevant to describe holographic properties of black holes with two equal angular momenta in five dimensions (with or without cosmological constant). We focus on the near-horizon geometry of the near-extremal black hole, where the effective theory reduces to Jackiw-Teitelboim (JT) gravity coupled to a massive scalar field. We compute the corrections to correlation functions due to cubic interactions present in this theory. A novel feature is that these corrections do not have a definite sign: for AdS$_5$ black holes the sign depends on the mass of the extremal solution. We discuss possible interpretations of these corrections from a gravitational and holographic perspective. We also quantify the imprint of the JT sector on the UV region, i.e. how these degrees of freedom, characteristic for the near-horizon region, influence the asymptotically far region of the black hole. This gives an interesting insight on how to interpret the IR modes in the context of their UV completion, which depends on the environment that contains the black hole.

  12 citations

• Emergent fractal phase in energy stratified random models

  Anton G. Kutlin, Ivan M. Khaymovich

  SciPost Phys. 11, 101 (2021) · published 6 December 2021 | Toggle abstract · pdf

  We study the effects of partial correlations in kinetic hopping terms of long-range disordered random matrix models on their localization properties. We consider a set of models interpolating between fully-localized Richardson's model and the celebrated Rosenzweig-Porter model (with implemented translation-invariant symmetry). In order to do this, we propose the energy-stratified spectral structure of the hopping term allowing one to decrease the range of correlations gradually. We show both analytically and numerically that any deviation from the completely correlated case leads to the emergent non-ergodic delocalization in the system unlike the predictions of localization of cooperative shielding. In order to describe the models with correlated kinetic terms, we develop the generalization of the Dyson Brownian motion and cavity approaches basing on stochastic matrix process with independent rank-one matrix increments and examine its applicability to the above set of models.

  15 citations

• Optical lattice with spin-dependent sub-wavelength barriers

  Edvinas Gvozdiovas, Povilas Račkauskas, Gediminas Juzeliūnas

  SciPost Phys. 11, 100 (2021) · published 2 December 2021 | Toggle abstract · pdf

  We analyze a tripod atom light coupling scheme characterized by two dark states playing the role of quasi-spin states. It is demonstrated that by properly configuring the coupling laser fields, one can create a lattice with spin-dependent sub-wavelength barriers. This allows to flexibly alter the atomic motion ranging from atomic dynamics in the effective brick-wall type lattice to free motion of atoms in one dark state and a tight binding lattice with a twice smaller periodicity for atoms in the other dark state. Between the two regimes, the spectrum undergoes significant changes controlled by the laser fields. The tripod lattice can be produced using current experimental techniques. The use of the tripod scheme to create a lattice of degenerate dark states opens new possibilities for spin ordering and symmetry breaking.

  3 citations

• GHZ-like states in the Qubit-Qudit Rabi model

  Yuan Shen, Giampiero Marchegiani, Gianluigi Catelani, Luigi Amico, Ai Qun Liu, Weijun Fan, Leong-Chuan Kwek

  SciPost Phys. 11, 099 (2021) · published 1 December 2021 | Toggle abstract · pdf

  We study a Rabi type Hamiltonian system in which a qubit and a d-level quantum system (qudit) are coupled through a common resonator. In the weak and strong coupling limits the spectrum is analysed through suitable perturbative schemes. The analysis show that the presence of the multilevels of the qudit effectively enhance the qubit-qudit interaction. The ground state of the strongly coupled system is found to be of Greenberger-Horne-Zeilinger (GHZ) type. Therefore, despite the qubit-qudit strong coupling, the nature of the specific tripartite entanglement of the GHZ state suppresses the bipartite entanglement. We analyze the system dynamics under quenching and adiabatic switching of the qubit-resonator and qudit-resonator couplings. In the quench case, we found that the non-adiabatic generation of photons in the resonator is enhanced by the number of levels in the qudit. The adiabatic control represents a possible route for preparation of GHZ states. Our analysis provides relevant information for future studies on coherent state transfer in qubit-qudit systems.

  3 citations

• Quantum approximate optimization for hard problems in linear algebra

  Ajinkya Borle, Vincent E. Elfving, Samuel J. Lomonaco

  SciPost Phys. Core 4, 031 (2021) · published 30 November 2021 | Toggle abstract · pdf

  The quantum approximate optimization algorithm (QAOA) by Farhi et al. is a quantum computational framework for solving quantum or classical optimization tasks. Here, we explore using QAOA for binary linear least squares (BLLS); a problem that can serve as a building block of several other hard problems in linear algebra, such as the non-negative binary matrix factorization (NBMF) and other variants of the non-negative matrix factorization (NMF) problem. Most of the previous efforts in quantum computing for solving these problems were done using the quantum annealing paradigm. For the scope of this work, our experiments were done on noiseless quantum simulators, a simulator including a device-realistic noise-model, and two IBM Q 5-qubit machines. We highlight the possibilities of using QAOA and QAOA-like variational algorithms for solving such problems, where trial solutions can be obtained directly as samples, rather than being amplitude-encoded in the quantum wavefunction. Our numerics show that even for a small number of steps, simulated annealing can outperform QAOA for BLLS at a QAOA depth of $p\leq3$ for the probability of sampling the ground state. Finally, we point out some of the challenges involved in current-day experimental implementations of this technique on cloud-based quantum computers.

  9 citations

• The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study

  Philipp Schmoll, Augustine Kshetrimayum, Jens Eisert, Román Orús, Matteo Rizzi

  SciPost Phys. 11, 098 (2021) · published 29 November 2021 | Toggle abstract · pdf

  The classical Heisenberg model in two spatial dimensions constitutes one of the most paradigmatic spin models, taking an important role in statistical and condensed matter physics to understand magnetism. Still, despite its paradigmatic character and the widely accepted ban of a (continuous) spontaneous symmetry breaking, controversies remain whether the model exhibits a phase transition at finite temperature. Importantly, the model can be interpreted as a lattice discretization of the $O(3)$ non-linear sigma model in $1+1$ dimensions, one of the simplest quantum field theories encompassing crucial features of celebrated higher-dimensional ones (like quantum chromodynamics in $3+1$ dimensions), namely the phenomenon of asymptotic freedom. This should also exclude finite-temperature transitions, but lattice effects might play a significant role in correcting the mainstream picture. In this work, we make use of state-of-the-art tensor network approaches, representing the classical partition function in the thermodynamic limit over a large range of temperatures, to comprehensively explore the correlation structure for Gibbs states. By implementing an $SU(2)$ symmetry in our two-dimensional tensor network contraction scheme, we are able to handle very large effective bond dimensions of the environment up to $\chi_E^\text{eff} \sim 1500$, a feature that is crucial in detecting phase transitions. With decreasing temperatures, we find a rapidly diverging correlation length, whose behaviour is apparently compatible with the two main contradictory hypotheses known in the literature, namely a finite-$T$ transition and asymptotic freedom, though with a slight preference for the second.

  6 citations

• The one-loop tadpole in the geoSMEFT

  Tyler Corbett

  SciPost Phys. 11, 097 (2021) · published 26 November 2021 | Toggle abstract · pdf

  Making use of the geometric formulation of the Standard Model Effective Field Theory we calculate the one-loop tadpole diagrams to all orders in the Standard Model Effective Field Theory power counting. This work represents the first calculation of a one-loop amplitude beyond leading order in the Standard Model Effective Field Theory, and discusses the potential to extend this methodology to perform similar calculations of observables in the near future.

  4 citations

• 1-form symmetries of 4d N=2 class S theories

  Lakshya Bhardwaj, Max Hübner, Sakura Schäfer-Nameki

  SciPost Phys. 11, 096 (2021) · published 24 November 2021 | Toggle abstract · pdf

  We determine the 1-form symmetry group for any 4d N = 2 class S theory constructed by compactifying a 6d N=(2,0) SCFT on a Riemann surface with arbitrary regular untwisted and twisted punctures. The 6d theory has a group of mutually non-local dimension-2 surface operators, modulo screening. Compactifying these surface operators leads to a group of mutually non-local line operators in 4d, modulo screening and flavor charges. Complete specification of a 4d theory arising from such a compactification requires a choice of a maximal subgroup of mutually local line operators, and the 1-form symmetry group of the chosen 4d theory is identified as the Pontryagin dual of this maximal subgroup. We also comment on how to generalize our results to compactifications involving irregular punctures. Finally, to complement the analysis from 6d, we derive the 1-form symmetry from a Type IIB realization of class S theories.

  38 citations