Publications

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• 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

• Fermi-gas correlators of ADHM theory and triality symmetry

  Yasuyuki Hatsuda, Tadashi Okazaki

  SciPost Phys. 12, 005 (2022) · published 5 January 2022 | Toggle abstract · pdf

  We analytically study the Fermi-gas formulation of sphere correlation functions of the Coulomb branch operators for 3d $\mathcal{N}=4$ ADHM theory with a gauge group $U(N)$, an adjoint hypermultiplet and $l$ hypermultiplets which can describe a stack of $N$ M2-branes at $A_{l-1}$ singularities. We find that the leading coefficients of the perturbative grand canonical correlation functions are invariant under a hidden triality symmetry conjectured from the twisted M-theory. The triality symmetry also helps us to fix the next-to-leading corrections analytically.

  6 citations

• Page curve for entanglement negativity through geometric evaporation

  Jaydeep Kumar Basak, Debarshi Basu, Vinay Malvimat, Himanshu Parihar, Gautam Sengupta

  SciPost Phys. 12, 004 (2022) · published 5 January 2022 | Toggle abstract · pdf

  We compute the entanglement negativity for various pure and mixed state configurations in a bath coupled to an evaporating two dimensional non-extremal Jackiw-Teitelboim (JT) black hole obtained through the partial dimensional reduction of a three dimensional BTZ black hole. Our results exactly reproduce the analogues of the Page curve for the entanglement negativity which were recently determined through diagrammatic technique developed in the context of random matrix theory.

  19 citations

• Islands for entanglement negativity

  Jaydeep Kumar Basak, Debarshi Basu, Vinay Malvimat, Himanshu Parihar, Gautam Sengupta

  SciPost Phys. 12, 003 (2022) · published 5 January 2022 | Toggle abstract · pdf

  We advance two alternative proposals for the island contributions to the entanglement negativity of various pure and mixed state configurations in quantum field theories coupled to semiclassical gravity. The first construction involves the extremization of an algebraic sum of the generalized Renyi entropies of order half. The second proposal involves the extremization of the sum of the effective entanglement negativity of quantum matter fields and the backreacted area of a cosmic brane spanning the entanglement wedge cross section which also extremizes the generalized Renyi reflected entropy of order half. These proposals are utilized to obtain the island contributions to the entanglement negativity of various pure and mixed state configurations involving the bath systems coupled to extremal and non-extremal black holes in JT gravity demonstrating an exact match with each other. Furthermore, the results from both the proposals match precisely with the island contribution to half the Renyi reflected entropy of order half providing a strong consistency check. We then allude to a possible doubly holographic picture of our island proposals and provide a derivation of the first proposal by determining the corresponding replica wormhole contributions.

  37 citations

• Quantum fidelity susceptibility in excited state quantum phase transitions: application to the bending spectra of nonrigid molecules

  Jamil Khalouf-Rivera, Miguel Carvajal, Francisco Pérez-Bernal

  SciPost Phys. 12, 002 (2022) · published 4 January 2022 | Toggle abstract · pdf

  We characterize excited state quantum phase transitions in the two dimensional limit of the vibron model with the quantum fidelity susceptibility, comparing the obtained results with the information provided by the participation ratio. As an application, we locate the eigenstate closest to the barrier to linearity and determine the linear or bent character of the different overtones for particular bending modes of six molecular species. We perform a fit and use the optimized eigenvalues and eigenstates in three cases and make use of recently published results for the other three cases.

  7 citations

• Reconstructing the graviton

  Alfio Bonanno, Tobias Denz, Jan M. Pawlowski, Manuel Reichert

  SciPost Phys. 12, 001 (2022) · published 4 January 2022 | Toggle abstract · pdf

  We reconstruct the Lorentzian graviton propagator in asymptotically safe quantum gravity from Euclidean data. The reconstruction is applied to both the dynamical fluctuation graviton and the background graviton propagator. We prove that the spectral function of the latter necessarily has negative parts similar to, and for the same reasons, as the gluon spectral function. In turn, the spectral function of the dynamical graviton is positive. We argue that the latter enters cross sections and other observables in asymptotically safe quantum gravity. Hence, its positivity may hint at the unitarity of asymptotically safe quantum gravity.

  42 citations

• A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions

  Yin-Chen He, Junchen Rong, Ning Su

  SciPost Phys. 11, 111 (2021) · published 22 December 2021 | Toggle abstract · pdf

  We propose a roadmap for bootstrapping conformal field theories (CFTs) described by gauge theories in dimensions $d>2$. In particular, we provide a simple and workable answer to the question of how to detect the gauge group in the bootstrap calculation. Our recipe is based on the notion of \emph{decoupling operator}, which has a simple (gauge) group theoretical origin, and is reminiscent of the null operator of $2d$ Wess-Zumino-Witten CFTs in higher dimensions. Using the decoupling operator we can efficiently detect the rank (i.e. color number) of gauge groups, e.g., by imposing gap conditions in the CFT spectrum. We also discuss the physics of the equation of motion, which has interesting consequences in the CFT spectrum as well. As an application of our recipes, we study a prototypical critical gauge theory, namely the scalar QED which has a $U(1)$ gauge field interacting with critical bosons. We show that the scalar QED can be solved by conformal bootstrap, namely we have obtained its kinks and islands in both $d=3$ and $d=2+\epsilon$ dimensions.

  8 citations

• Full counting statistics for interacting trapped fermions

  Naftali R. Smith, Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr

  SciPost Phys. 11, 110 (2021) · published 22 December 2021 | Toggle abstract · pdf

  We study $N$ spinless fermions in their ground state confined by an external potential in one dimension with long range interactions of the general Calogero-Sutherland type. For some choices of the potential this system maps to standard random matrix ensembles for general values of the Dyson index $\beta$. In the fermion model $\beta$ controls the strength of the interaction, $\beta=2$ corresponding to the noninteracting case. We study the quantum fluctuations of the number of fermions ${\cal N}_{\cal D}$ in a domain $\cal{D}$ of macroscopic size in the bulk of the Fermi gas. We predict that for general $\beta$ the variance of ${\cal N}_{\cal D}$ grows as $A_{\beta} \log N + B_{\beta}$ for $N \gg 1$ and we obtain a formula for $A_\beta$ and $B_\beta$. This is based on an explicit calculation for $\beta\in\left\{ 1,2,4\right\} $ and on a conjecture that we formulate for general $\beta$. This conjecture further allows us to obtain a universal formula for the higher cumulants of ${\cal N}_{\cal D}$. Our results for the variance in the microscopic regime are found to be consistent with the predictions of the Luttinger liquid theory with parameter $K = 2/\beta$, and allow to go beyond. In addition we present families of interacting fermion models in one dimension which, in their ground states, can be mapped onto random matrix models. We obtain the mean fermion density for these models for general interaction parameter $\beta$. In some cases the fermion density exhibits interesting transitions, for example we obtain a noninteracting fermion formulation of the Gross-Witten-Wadia model.

  14 citations

• Engineering spectral properties of non-interacting lattice Hamiltonians

  Ali G. Moghaddam, Dmitry Chernyavsky, Corentin Morice, Jasper van Wezel, Jeroen van den Brink

  SciPost Phys. 11, 109 (2021) · published 22 December 2021 | Toggle abstract · pdf

  We investigate the spectral properties of one-dimensional lattices with position-dependent hopping amplitudes and on-site potentials that are smooth bounded functions of the position. We find an exact integral form for the density of states (DOS) in the limit of an infinite number of sites, which we derive using a mixed Bloch-Wannier basis consisting of piecewise Wannier functions. Next, we provide an exact solution for the inverse problem of constructing the position-dependence of hopping in a lattice model yielding a given DOS. We confirm analytic results by comparing them to numerics obtained by exact diagonalization for various incarnations of position-dependent hoppings and on-site potentials. Finally, we generalize the DOS integral form to multi-orbital tight-binding models with longer-range hoppings and in higher dimensions.

  4 citations

• Conserved momenta of ferromagnetic solitons through the prism of differential geometry

  Xingjian Di, Oleg Tchernyshyov

  SciPost Phys. 11, 108 (2021) · published 21 December 2021 | Toggle abstract · pdf

  The relation between symmetries and conservation laws for solitons in a ferromagnet is complicated by the presence of gyroscopic (precessional) forces, whose description in the Lagrangian framework involves a background gauge field. This makes canonical momenta gauge-dependent and requires a careful application of Noether's theorem. We show that Cartan's theory of differential forms is a natural language for this task. We use it to derive conserved momenta of the Belavin--Polyakov skyrmion, whose symmetries include translation, global spin rotation, and dilation.

  3 citations