Publications

Order by: publication date number of citations

• Circuit Complexity through phase transitions: Consequences in quantum state preparation

  Sebastián Roca-Jerat, Teresa Sancho-Lorente, Juan Román-Roche, David Zueco

  SciPost Phys. 15, 186 (2023) · published 8 November 2023 | Toggle abstract · pdf

  In this paper, we analyze the circuit complexity for preparing ground states of quantum many-body systems. In particular, how this complexity grows as the ground state approaches a quantum phase transition. We discuss different definitions of complexity, namely the one following the Fubini-Study metric or the Nielsen complexity. We also explore different models: Ising, ZZXZ or Dicke. In addition, different forms of state preparation are investigated: analytic or exact diagonalization techniques, adiabatic algorithms (with and without shortcuts), and Quantum Variational Eigensolvers. We find that the divergence (or lack thereof) of the complexity near a phase transition depends on the non-local character of the operations used to reach the ground state. For Fubini-Study based complexity, we extract the universal properties and their critical exponents. In practical algorithms, we find that the complexity depends crucially on whether or not the system passes close to a quantum critical point when preparing the state. For both VQE and Adiabatic algorithms, we provide explicit expressions and bound the growth of complexity with respect to the system size and the execution time, respectively.

  8 citations

• Universal scaling of quench-induced correlations in a one-dimensional channel at finite temperature

  Alessio Calzona, Filippo Maria Gambetta, Matteo Carrega, Fabio Cavaliere, Thomas L. Schmidt, Maura Sassetti

  SciPost Phys. 4, 023 (2018) · published 10 May 2018 | Toggle abstract · pdf

  It has been shown that a quantum quench of interactions in a one-dimensional fermion system at zero temperature induces a universal power law $\propto t^{-2}$ in its long-time dynamics. In this paper we demonstrate that this behaviour is robust even in the presence of thermal effects. The system is initially prepared in a thermal state, then at a given time the bath is disconnected and the interaction strength is suddenly quenched. The corresponding effects on the long times dynamics of the non-equilibrium fermionic spectral function are considered. We show that the non-universal power laws, present at zero temperature, acquire an exponential decay due to thermal effects and are washed out at long times, while the universal behaviour $\propto t^{-2}$ is always present. To verify our findings, we argue that these features are also visible in transport properties at finite temperature. The long-time dynamics of the current injected from a biased probe exhibits the same universal power law relaxation, in sharp contrast with the non-quenched case which features a fast exponential decay of the current towards its steady value, and thus represents a fingerprint of quench-induced dynamics. Finally, we show that a proper tuning of the probe temperature, compared to that of the one-dimensional channel, can enhance the visibility of the universal power-law behaviour.

  8 citations

• Quantum current and holographic categorical symmetry

  Tian Lan, Jing-Ren Zhou

  SciPost Phys. 16, 053 (2024) · published 23 February 2024 | Toggle abstract · pdf

  We establish the formulation for quantum current. Given a symmetry group G, let $\mathcal{C}$:=Rep G be its representation category. Physically, symmetry charges are objects of $\mathcal{C}$ and symmetric operators are morphisms in $\mathcal{C}$. The addition of charges is given by the tensor product of representations. For any symmetric operator O crossing two subsystems, the exact symmetry charge transported by O can be extracted. The quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. A quantum current exactly corresponds to an object in the Drinfeld center $Z_1(\mathcal{C})$. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension. To express the local conservation, the internal hom must be used to compute the charge difference, and the framework of enriched category is inevitable. To illustrate these ideas, we develop a rigorous scheme of renormalization in one-dimensional lattice systems and analyse the fixed-point models. It is proved that in the fixed-point models, superconducting quantum currents form a Lagrangian algebra in $Z_1(\mathcal{C})$ and the boundary-bulk correspondence is verified in the enriched setting. Overall, the quantum current provides a natural physical interpretation to the holographic categorical symmetry.

  8 citations

• Entanglement and interaction in a topological quantum walk

  Alberto D. Verga, Ricardo Gabriel Elias

  SciPost Phys. 5, 019 (2018) · published 31 August 2018 | Toggle abstract · pdf

  We study the quantum walk of two interacting particles on a line with an interface separating two topologically distinct regions. The interaction induces a localization-delocalization transition of the edge state at the interface. We characterize the transition through the entanglement between the two particles.

  8 citations

• Phase separation in binary Bose mixtures at finite temperature

  Gabriele Spada, Luca Parisi, Gerard Pascual, Nicholas G. Parker, Thomas P. Billam, Sebastiano Pilati, Jordi Boronat, Stefano Giorgini

  SciPost Phys. 15, 171 (2023) · published 18 October 2023 | Toggle abstract · pdf

  We investigate the magnetic behavior of finite-temperature repulsive two-component Bose mixtures by means of exact path-integral Monte-Carlo simulations. Novel algorithms are implemented for the free energy and the chemical potential of the two components. Results on the magnetic susceptibility suggest that the conditions for phase separation are not modified from the zero temperature case. This contradicts previous predictions based on approximate theories. We also determine the temperature dependence of the chemical potential and the contact parameters for experimentally relevant balanced mixtures.

  8 citations

• Efficient flow equations for dissipative systems

  Gary Schmiedinghoff, Götz S. Uhrig

  SciPost Phys. 13, 122 (2022) · published 13 December 2022 | Toggle abstract · pdf

  Open quantum systems provide an essential theoretical basis for the development of novel quantum technologies, since any real quantum system inevitably interacts with its environment. Lindblad master equations capture the effect of Markovian environments. Closed quantum systems can be treated using flow equations with the particle conserving generator. We generalize this generator to non-Hermitian matrices and open quantum systems governed by Lindbladians, comparing our results with recently proposed generators by Rosso et al. (arXiv:2007.12044). In comparison, we find that our advocated generator provides an efficient flow with good accuracy in spite of truncations.

  8 citations

• Entanglement entropy with Lifshitz fermions

  Dion Hartmann, Kevin Kavanagh, Stefan Vandoren

  SciPost Phys. 11, 031 (2021) · published 17 August 2021 | Toggle abstract · pdf

  We investigate fermions with Lifshitz scaling symmetry and study their entanglement entropy in 1+1 dimensions as a function of the scaling exponent $z$. Remarkably, in the ground state the entanglement entropy vanishes for even values of $z$, whereas for odd values it is independent of $z$ and equal to the relativistic case with $z=1$. We show this using the correlation method on the lattice, and also using a holographic cMERA approach. The entanglement entropy in a thermal state is a more detailed function of $z$ and $T$ which we plot using the lattice correlation method. The dependence on the even- or oddness of $z$ still shows for small temperatures, but is washed out for large temperatures or large values of $z$.

  8 citations

• Multipole groups and fracton phenomena on arbitrary crystalline lattices

  Daniel Bulmash, Oliver Hart, Rahul Nandkishore

  SciPost Phys. 15, 235 (2023) · published 12 December 2023 | Toggle abstract · pdf

  Multipole symmetries are of interest in multiple contexts, from the study of fracton phases, to nonergodic quantum dynamics, to the exploration of new hydrodynamic universality classes. However, prior explorations have focused on continuum systems or hypercubic lattices. In this work, we systematically explore multipole symmetries on arbitrary crystal lattices. We explain how, given a crystal structure (specified by a space group and the occupied Wyckoff positions), one may systematically construct all consistent multipole groups. We focus on two-dimensional crystal structures for simplicity, although our methods are general and extend straightforwardly to three dimensions. We classify the possible multipole groups on all two-dimensional Bravais lattices, and on the Kagome and breathing Kagome crystal structures to illustrate the procedure on general crystal lattices. Using Wyckoff positions, we provide an in-principle classification of all possible multipole groups in any space group. We explain how, given a valid multipole group, one may construct a consistent lattice Hamiltonian and a low-energy field theory. We then explore the physical consequences, beginning by generalizing certain results originally obtained on hypercubic lattices to arbitrary crystal structures. Next, we identify two apparently novel phenomena: an emergent, robust subsystem symmetry on the triangular lattice, and an exact multipolar symmetry on the breathing Kagome lattice that does not include conservation of charge (monopole), but instead conserves a vector charge. This makes clear that there is new physics to be found by exploring the consequences of multipolar symmetries on arbitrary lattices, and this work provides the map for the exploration thereof, as well as guiding the search for emergent multipolar symmetries and the attendant exotic phenomena in real materials based on nonhypercubic lattices.

  8 citations

• Visibility of noisy quantum dot-based measurements of Majorana qubits

  Aleksei Khindanov, Dmitry Pikulin, Torsten Karzig

  SciPost Phys. 10, 127 (2021) · published 2 June 2021 | Toggle abstract · pdf

  Measurement schemes of Majorana zero modes (MZMs) based on quantum dots (QDs) are of current interest as they provide a scalable platform for topological quantum computation. In a coupled qubit-QD setup we calculate the dependence of the charge of the QD and its differential capacitance on experimentally tunable parameters for both 2-MZM and 4-MZM measurements. We quantify the effect of noise on the measurement visibility by considering $1/f$ noise in detuning, tunneling amplitudes or phase. We find that on- or close-to-resonance measurements are generally preferable and predict, using conservative noise estimates, that noise coupling to the QDs is not a limitation to high-fidelity measurements of topological qubits.

  8 citations

• Collective Monte Carlo updates through tensor network renormalization

  Miguel Frías-Pérez, Michael Mariën, David Pérez García, Mari Carmen Bañuls, Sofyan Iblisdir

  SciPost Phys. 14, 123 (2023) · published 22 May 2023 | Toggle abstract · pdf

  We introduce a Metropolis-Hastings Markov chain for Boltzmann distributions of classical spin systems. It relies on approximate tensor network contractions to propose correlated collective updates at each step of the evolution. We present benchmark computations for a wide variety of instances of the two-dimensional Ising model, including ferromagnetic, antiferromagnetic, (fully) frustrated and Edwards-Anderson spin glass instances, and we show that, with modest computational effort, our Markov chain achieves sizeable acceptance rates, even in the vicinity of critical points. In each of the situations we have considered, the Markov chain compares well with other Monte Carlo schemes such as the Metropolis or Wolff's algorithm: equilibration times appear to be reduced by a factor that varies between $40$ and $2000$, depending on the model and the observable being monitored. We also present an extension to three spatial dimensions, and demonstrate that it exhibits fast equilibration for finite ferro- and antiferromagnetic instances. Additionally, and although it is originally designed for a square lattice of finite degrees of freedom with open boundary conditions, the proposed scheme can be used as such, or with slight modifications, to study triangular lattices, systems with continuous degrees of freedom, matrix models, a confined gas of hard spheres, or to deal with arbitrary boundary conditions.

  8 citations