Publications

Order by: publication date number of citations

• Abelian and non-abelian symmetries in infinite projected entangled pair states

  Claudius Hubig

  SciPost Phys. 5, 047 (2018) · published 9 November 2018 | Toggle abstract · pdf

  We explore in detail the implementation of arbitrary abelian and non-abelian symmetries in the setting of infinite projected entangled pair states on the two-dimensional square lattice. We observe a large computational speed-up; easily allowing bond dimensions $D = 10$ in the square lattice Heisenberg model at computational effort comparable to calculations at $D = 6$ without symmetries. We also find that implementing an unbroken symmetry does not negatively affect the representative power of the state and leads to identical or improved ground-state energies. Finally, we point out how to use symmetry implementations to detect spontaneous symmetry breaking.

  16 citations

• Projective phase measurements in one-dimensional Bose gases

  Yuri D. van Nieuwkerk, Jörg Schmiedmayer, Fabian H. L. Essler

  SciPost Phys. 5, 046 (2018) · published 8 November 2018 | Toggle abstract · pdf

  We consider time-of-flight measurements in split one-dimensional Bose gases. It is well known that the low-energy sector of such systems can be described in terms of two compact phase fields $\hat{\phi}_{a,s}(x)$. Building on existing results in the literature we discuss how a single projective measurement of the particle density after trap release is in a certain limit related to the eigenvalues of the vertex operator $e^{i\hat{\phi}_a(x)}$. We emphasize the theoretical assumptions underlying the analysis of "single-shot" interference patterns and show that such measurements give direct access to multi-point correlation functions of $e^{i\hat{\phi}_a(x)}$ in a substantial parameter regime. For experimentally relevant situations, we derive an expression for the measured particle density after trap release in terms of convolutions of the eigenvalues of vertex operators involving both sectors of the two-component Luttinger liquid that describes the low-energy regime of the split condensate. This opens the door to accessing properties of the symmetric sector via an appropriate analysis of existing experimental data.

  20 citations

• Shift-invert diagonalization of large many-body localizing spin chains

  Francesca Pietracaprina, Nicolas Macé, David J. Luitz, Fabien Alet

  SciPost Phys. 5, 045 (2018) · published 6 November 2018 | Toggle abstract · pdf

  We provide a pedagogical review on the calculation of highly excited eigenstates of disordered interacting quantum systems which can undergo a many-body localization (MBL) transition, using shift-invert exact diagonalization. We also provide an example code at https://bitbucket.org/dluitz/sinvert_mbl/. Through a detailed analysis of the simulational parameters of the random field Heisenberg spin chain, we provide a practical guide on how to perform efficient computations. We present data for mid-spectrum eigenstates of spin chains of sizes up to $L=26$. This work is also geared towards readers with interest in efficiency of parallel sparse linear algebra techniques that will find a challenging application in the MBL problem.

  89 citations

• Cooling phonon modes of a Bose condensate with uniform few body losses

  Isabelle Bouchoule, Max Schemmer, Carsten Henkel

  SciPost Phys. 5, 043 (2018) · published 2 November 2018 | Toggle abstract · pdf

  We present a general analysis of the cooling produced by losses on condensates or quasi-condensates. We study how the occupations of the collective phonon modes evolve in time, assuming that the loss process is slow enough so that each mode adiabatically follows the decrease of the mean density. The theory is valid for any loss process whose rate is proportional to the $j$th power of the density, but otherwise spatially uniform. We cover both homogeneous gases and systems confined in a smooth potential. For a low-dimensional gas, we can take into account the modified equation of state due to the broadening of the cloud width along the tightly confined directions, which occurs for large interactions. We find that at large times, the temperature decreases proportionally to the energy scale $mc^2$, where $m$ is the mass of the particles and $c$ the sound velocity. We compute the asymptotic ratio of these two quantities for different limiting cases: a homogeneous gas in any dimension and a one-dimensional gas in a harmonic trap.

  10 citations

• Monitoring continuous spectrum observables: the strong measurement limit

  Michel Bauer, Denis Bernard, Tony Jin

  SciPost Phys. 5, 037 (2018) · published 24 October 2018 | Toggle abstract · pdf

  We revisit aspects of monitoring observables with continuous spectrum in a quantum system subject to dissipative (Lindbladian) or conservative (Hamiltonian) evolutions. After recalling some of the salient features of the case of pure monitoring, we deal with the case when monitoring is in competition with a Lindbladian evolution. We show that the strong measurement limit leads to a diffusion on the spectrum of the observable. For the case with competition between observation and Hamiltonian dynamics, we exhibit a scaling limit in which the crossover between the classical regime and a diffusive regime can be analyzed in details.

  3 citations

• Spreading of entanglement and correlations after a quench with intertwined quasiparticles

  Alvise Bastianello, Pasquale Calabrese

  SciPost Phys. 5, 033 (2018) · published 15 October 2018 | Toggle abstract · pdf

  We extend the semiclassical picture for the spreading of entanglement and correlations to quantum quenches with several species of quasiparticles that have non-trivial pair correlations in momentum space. These pair correlations are, for example, relevant in inhomogeneous lattice models with a periodically-modulated Hamiltonian parameter. We provide explicit predictions for the spreading of the entanglement entropy in the space-time scaling limit. We also predict the time evolution of one- and two-point functions of the order parameter for quenches within the ordered phase. We test all our predictions against exact numerical results for quenches in the Ising chain with a modulated transverse field and we find perfect agreement.

  45 citations

• Counterdiabatic Hamiltonians for multistate Landau-Zener problem

  Kohji Nishimura, Kazutaka Takahashi

  SciPost Phys. 5, 029 (2018) · published 27 September 2018 | Toggle abstract · pdf

  We study the Landau-Zener transitions generalized to multistate systems. Based on the work by Sinitsyn et al. [Phys. Rev. Lett. 120, 190402 (2018)], we introduce the auxiliary Hamiltonians that are interpreted as the counterdiabatic terms. We find that the counterdiabatic Hamiltonians satisfy the zero curvature condition. The general structures of the auxiliary Hamiltonians are studied in detail and the time-evolution operator is evaluated by using a deformation of the integration contour and asymptotic forms of the auxiliary Hamiltonians. For several spin models with transverse field, we calculate the transition probability between the initial and final ground states and find that the method is useful to study nonadiabatic regime.

  5 citations

• Quantifying the effect of interactions in quantum many-body systems

  Jiannis K. Pachos, Zlatko Papic

  SciPost Phys. Lect. Notes 4 (2018) · published 27 September 2018 | Toggle abstract · pdf

  Free fermion systems enjoy a privileged place in physics. With their simple structure they can explain a variety of effects, ranging from insulating and metallic behaviours to superconductivity and the integer quantum Hall effect. Interactions, e.g. in the form of Coulomb repulsion, can dramatically alter this picture by giving rise to emerging physics that may not resemble free fermions. Examples of such phenomena include high-temperature superconductivity, fractional quantum Hall effect, Kondo effect and quantum spin liquids. The non-perturbative behaviour of such systems remains a major obstacle to their theoretical understanding that could unlock further technological applications. Here, we present a pedagogical review of "interaction distance" [Nat. Commun. 8, 14926 (2017)] -- a systematic method that quantifies the effect interactions can have on the energy spectrum and on the quantum correlations of generic many-body systems. In particular, the interaction distance is a diagnostic tool that identifies the emergent physics of interacting systems. We illustrate this method on the simple example of a one-dimensional Fermi-Hubbard dimer.

  9 citations

• Quench dynamics of the Ising field theory in a magnetic field

  Kristóf Hódsági, Márton Kormos, Gábor Takács

  SciPost Phys. 5, 027 (2018) · published 25 September 2018 | Toggle abstract · pdf

  We numerically simulate the time evolution of the Ising field theory after quenches starting from the $E_8$ integrable model using the Truncated Conformal Space Approach. The results are compared with two different analytic predictions based on form factor expansions in the pre-quench and post-quench basis, respectively. Our results clarify the domain of validity of these expansions and suggest directions for further improvement. We show for quenches in the $E_8$ model that the initial state is not of the integrable pair state form. We also construct quench overlap functions and show that their high-energy asymptotics are markedly different from those constructed before in the sinh/sine-Gordon theory, and argue that this is related to properties of the ultraviolet fixed point.

  32 citations

• Scale invariant distribution functions in quantum systems with few degrees of freedom

  Emanuele G. Dalla Torre

  SciPost Phys. 5, 023 (2018) · published 14 September 2018 | Toggle abstract · pdf

  Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At equilibrium these functions decay over a typical scale set by the temperature, but they can become scale invariant in a sudden quantum quench. We exemplify this effect through the analysis of linear and non-linear quantum oscillators. We find that their distribution functions generically diverge logarithmically close to the stable points of the classical dynamics. Our study opens the possibility to address integrability and its breaking in distribution functions, with immediate applications to matter-wave interferometers.

  1 citation