Publications

Order by: publication date number of citations

• Automatic differentiation applied to excitations with projected entangled pair states

  Boris Ponsioen, Fakher F. Assaad, Philippe Corboz

  SciPost Phys. 12, 006 (2022) · published 6 January 2022 | Toggle abstract · pdf

  The excitation ansatz for tensor networks is a powerful tool for simulating the low-lying quasiparticle excitations above ground states of strongly correlated quantum many-body systems. Recently, the two-dimensional tensor network class of infinite entangled pair states gained new ground state optimization methods based on automatic differentiation, which are at the same time highly accurate and simple to implement. Naturally, the question arises whether these new ideas can also be used to optimize the excitation ansatz, which has recently been implemented in two dimensions as well. In this paper, we describe a straightforward way to reimplement the framework for excitations using automatic differentiation, and demonstrate its performance for the Hubbard model at half filling.

  19 citations

• Entanglement wedge in flat holography and entanglement negativity

  Debarshi Basu, Ashish Chandra, Vinayak Raj, Gautam Sengupta

  SciPost Phys. Core 5, 013 (2022) · published 15 March 2022 | Toggle abstract · pdf

  We establish a construction for the entanglement wedge in asymptotically flat bulk geometries for subsystems in dual $(1+1)$-dimensional Galilean conformal field theories in the context of flat space holography. In this connection we propose a definition for the bulk entanglement wedge cross section for bipartite states of such dual non relativistic conformal field theories. Utilizing our construction for the entanglement wedge cross section we compute the entanglement negativity for such bipartite states through the generalization of an earlier proposal, in the context of the usual $AdS/CFT$ scenario, to flat space holography. The entanglement negativity obtained from our construction exactly reproduces earlier holographic results and match with the corresponding field theory replica technique results in the large central charge limit.

  19 citations

• Conditions for fully gapped topological superconductivity in topological insulator nanowires

  Fernando de Juan, Jens H. Bardarson, Roni Ilan

  SciPost Phys. 6, 060 (2019) · published 17 May 2019 | Toggle abstract · pdf

  Among the different platforms to engineer Majorana fermions in one-dimensional topological superconductors, topological insulator nanowires remain a promising option. Threading an odd number of flux quanta through these wires induces an odd number of surface channels, which can then be gapped with proximity induced pairing. Because of the flux and depending on energetics, the phase of this surface pairing may or may not wind around the wire in the form of a vortex. Here we show that for wires with discrete rotational symmetry, this vortex is necessary to produce a fully gapped topological superconductor with localized Majorana end states. Without a vortex the proximitized wire remains gapless, and it is only if the symmetry is broken by disorder that a gap develops, which is much smaller than the one obtained with a vortex. These results are explained with the help of a continuum model and validated numerically with a tight binding model, and highlight the benefit of a vortex for reliable use of Majorana fermions in this platform.

  19 citations

• Relaxation of the order-parameter statistics in the Ising quantum chain

  Mario Collura

  SciPost Phys. 7, 072 (2019) · published 2 December 2019 | Toggle abstract · pdf

  We study the out-of-equilibrium probability distribution function of the local order parameter in the transverse field Ising quantum chain. Starting from a fully polarised state, the relaxation of the ferromagnetic order is analysed: we obtain a full analytical description of the late-time stationary distribution by means of a remarkable relation to the partition function of a 3-states classical model. Accordingly, depending on the phase whereto the post-quench Hamiltonian belongs, the probability distribution may locally retain memories of the initial long-range order. When quenching deep in the broken-symmetry phase, we show that the stationary order-parameter statistics is indeed related to that of the ground state. We highlight this connection by inspecting the ground-state equilibrium properties, where we propose an effective description based on the block-diagonal approximation of the $n$-point spin correlation functions.

  19 citations

• Holographic thermal correlators from supersymmetric instantons

  Matthew Dodelson, Alba Grassi, Cristoforo Iossa, Daniel Panea Lichtig, Alexander Zhiboedov

  SciPost Phys. 14, 116 (2023) · published 16 May 2023 | Toggle abstract · pdf

  We present an exact formula for the thermal scalar two-point function in four-dimensional holographic conformal field theories. The problem of finding it reduces to the analysis of the wave equation on the AdS-Schwarzschild background. The two-point function is computed from the connection coefficients of the Heun equation, which can be expressed in terms of the Nekrasov-Shatashvili partition function of an $SU(2)$ supersymmetric gauge theory with four fundamental hypermultiplets. The result is amenable to numerical evaluation upon truncating the number of instantons in the convergent expansion of the partition function. We also examine it analytically in various limits. At large spin the instanton expansion of the thermal two-point function directly maps to the light-cone bootstrap analysis of the heavy-light four-point function. Using this connection, we compute the OPE data of heavy-light double-twist operators. We compare our prediction to the perturbative results available in the literature and find perfect agreement.

  19 citations

• Information geometry in quantum field theory: lessons from simple examples

  Johanna Erdmenger, Kevin T. Grosvenor, Ro Jefferson

  SciPost Phys. 8, 073 (2020) · published 6 May 2020 | Toggle abstract · pdf

  Motivated by the increasing connections between information theory and high-energy physics, particularly in the context of the AdS/CFT correspondence, we explore the information geometry associated to a variety of simple systems. By studying their Fisher metrics, we derive some general lessons that may have important implications for the application of information geometry in holography. We begin by demonstrating that the symmetries of the physical theory under study play a strong role in the resulting geometry, and that the appearance of an AdS metric is a relatively general feature. We then investigate what information the Fisher metric retains about the physics of the underlying theory by studying the geometry for both the classical 2d Ising model and the corresponding 1d free fermion theory, and find that the curvature diverges precisely at the phase transition on both sides. We discuss the differences that result from placing a metric on the space of theories vs. states, using the example of coherent free fermion states. We compare the latter to the metric on the space of coherent free boson states and show that in both cases the metric is determined by the symmetries of the corresponding density matrix. We also clarify some misconceptions in the literature pertaining to different notions of flatness associated to metric and non-metric connections, with implications for how one interprets the curvature of the geometry. Our results indicate that in general, caution is needed when connecting the AdS geometry arising from certain models with the AdS/CFT correspondence, and seek to provide a useful collection of guidelines for future progress in this exciting area.

  19 citations

• On the construction of charged operators inside an eternal black hole

  Monica Guica, Daniel L. Jafferis

  SciPost Phys. 3, 016 (2017) · published 28 August 2017 | Toggle abstract · pdf

  We revisit the holographic construction of (approximately) local bulk operators inside an eternal AdS black hole in terms of operators in the boundary CFTs. If the bulk operator carries charge, the construction must involve a qualitatively new object: a Wilson line that stretches between the two boundaries of the eternal black hole. This operator - more precisely, its zero mode - cannot be expressed in terms of the boundary currents and only exists in entangled states dual to two-sided geometries, which suggests that it is a state-dependent operator. We determine the action of the Wilson line on the relevant subspaces of the total Hilbert space, and show that it behaves as a local operator from the point of view of either CFT. For the case of three bulk dimensions, we give explicit expressions for the charged bulk field and the Wilson line. Furthermore, we show that when acting on the thermofield double state, the Wilson line may be extracted from a limit of certain standard CFT operator expressions. We also comment on the relationship between the Wilson line and previously discussed mirror operators in the eternal black hole.

  19 citations

• Impurities in a one-dimensional Bose gas: the flow equation approach

  Fabian Brauneis, Hans-Werner Hammer, Mikhail Lemeshko, Artem G. Volosniev

  SciPost Phys. 11, 008 (2021) · published 13 July 2021 | Toggle abstract · pdf

  A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities. For a single mobile impurity, we use flow equations to validate the mean-field results obtained upon the Lee-Low-Pines transformation. We show that the mean-field approximation is accurate for all values of the boson-impurity interaction strength as long as the phase coherence length is much larger than the healing length of the condensate. For two static impurities, we calculate impurity-impurity interactions induced by the Bose gas. We find that leading order perturbation theory fails when boson-impurity interactions are stronger than boson-boson interactions. The mean-field approximation reproduces the flow equation results for all values of the boson-impurity interaction strength as long as boson-boson interactions are weak.

  18 citations

• Entanglement, non-hermiticity, and duality

  Li-Mei Chen, Shuai A. Chen, Peng Ye

  SciPost Phys. 11, 003 (2021) · published 9 July 2021 | Toggle abstract · pdf

  Usually duality process keeps energy spectrum invariant. In this paper, we provide a duality, which keeps entanglement spectrum invariant, in order to diagnose quantum entanglement of non-Hermitian non-interacting fermionic systems. We limit our attention to non-Hermitian systems with a complete set of biorthonormal eigenvectors and an entirely real energy spectrum. The original system has a reduced density matrix $\rho_\mathrm{o}$ and the real space is partitioned via a projecting operator $\mathcal{R}_{\mathrm o}$. After dualization, we obtain a new reduced density matrix $\rho_{\mathrm{d}}$ and a new real space projector $\mathcal{R}_{\mathrm d}$. Remarkably, entanglement spectrum and entanglement entropy keep invariant. Inspired by the duality, we defined two types of non-Hermitian models, upon $\mathcal R_{\mathrm{o}}$ is given. In type-I exemplified by the ``non-reciprocal model'', there exists at least one duality such that $\rho_{\mathrm{d}}$ is Hermitian. In other words, entanglement information of type-I non-Hermitian models with a given $\mathcal{R}_{\mathrm{o}}$ is entirely controlled by Hermitian models with $\mathcal{R}_{\mathrm{d}}$. As a result, we are allowed to apply known results of Hermitian systems to efficiently obtain entanglement properties of type-I models. On the other hand, the duals of type-II models, exemplified by ``non-Hermitian Su-Schrieffer-Heeger model'', are always non-Hermitian. For the practical purpose, the duality provides a potentially \textit{efficient} computation route to entanglement of non-Hermitian systems. Via connecting different models, the duality also sheds lights on either trivial or nontrivial role of non-Hermiticity played in quantum entanglement, paving the way to potentially systematic classification and characterization of non-Hermitian systems from the entanglement perspective.

  18 citations

• Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model

  Tommaso Micallo, Vittorio Vitale, Marcello Dalmonte, Pierre Fromholz

  SciPost Phys. Core 3, 012 (2020) · published 1 December 2020 | Toggle abstract · pdf

  We study the disconnected entanglement entropy, $S^D$, of the Su-Schrieffer-Heeger model. $S^D$ is a combination of both connected and disconnected bipartite entanglement entropies that removes all area and volume law contributions, and is thus only sensitive to the non-local entanglement stored within the ground state manifold. Using analytical and numerical computations, we show that $S^D$ behaves as a topological invariant, i.e., it is quantized to either $0$ or $2 \log (2)$ in the topologically trivial and non-trivial phases, respectively. These results also hold in the presence of symmetry-preserving disorder. At the second-order phase transition separating the two phases, $S^D$ displays a system-size scaling behavior akin to those of conventional order parameters, that allows us to compute entanglement critical exponents. To corroborate the topological origin of the quantized values of $S^D$, we show how the latter remain quantized after applying unitary time evolution in the form of a quantum quench, a characteristic feature of topological invariants.

  18 citations