Publications

Order by: publication date number of citations

• A functional-analysis derivation of the parquet equation

  Christian J. Eckhardt, Patrick Kappl, Anna Kauch, Karsten Held

  SciPost Phys. 15, 203 (2023) · published 24 November 2023 | Toggle abstract · pdf

  The parquet equation is an exact field-theoretic equation known since the 60s that underlies numerous approximations to solve strongly correlated Fermion systems. Its derivation previously relied on combinatorial arguments classifying all diagrams of the two-particle Green's function in terms of their (ir)reducibility properties. In this work we provide a derivation of the parquet equation solely employing techniques of functional analysis namely functional Legendre transformations and functional derivatives. The advantage of a derivation in terms of a straightforward calculation is twofold: (i) the quantities appearing in the calculation have a clear mathematical definition and interpretation as derivatives of the Luttinger-Ward functional; (ii) analogous calculations to the ones that lead to the parquet equation may be performed for higher-order Green's functions potentially leading to a classification of these in terms of their (ir)reducible components.

• Brane detectors of a dynamical phase transition in a driven CFT

  Suchetan Das, Bobby Ezhuthachan, Arnab Kundu, Somnath Porey, Baishali Roy, Krishnendu Sengupta

  SciPost Phys. 15, 202 (2023) · published 23 November 2023 | Toggle abstract · pdf

  We show that a dynamical transition from a non-heating to a heating phase of a periodic $SL(2,\mathbb{R})$ driven two dimensional conformal field theory (CFT) with a large central charge is perceived as a first order transition by a bulk brane embedded in the dual AdS. We construct the dual bulk metric corresponding to a driven CFT for both the heating and the non-heating phases. These metrics are different AdS$_2$ slices of the pure AdS$_3$ metric. We embed a brane in the obtained dual AdS space and provide an explicit computation of its free energy both in the probe limit and for an end-of-world (EOW) brane taking into account its backreaction. Our analysis indicates a finite discontinuity in the first derivative of the brane free energy as one moves from the non-heating to the heating phase (by tuning the drive amplitude and/or frequency of the driven CFT) thus demonstrating the presence of the bulk first order transition. Interestingly, no such transition is perceived by the bulk in the absence of the brane. We also provide explicit computations of two-point, four-point out-of-time correlators (OTOC) using the bulk picture. Our analysis shows that the structure of these correlators in different phases match their counterparts computed in the driven CFT. We analyze the effect of multiple EOW branes in the bulk and discuss possible extensions of our work for richer geometries and branes.

  4 citations

• BRST invariant formulation of the Bell-CHSH inequality in gauge field theories

  David Dudal, Philipe De Fabritiis, Marcelo Santos Guimaraes, Giovani Peruzzo, Silvio Paolo Sorella

  SciPost Phys. 15, 201 (2023) · published 23 November 2023 | Toggle abstract · pdf

  A study of the Bell-CHSH inequality in gauge field theories is presented. By using the Kugo-Ojima analysis of the BRST charge cohomology in Fock space, the Bell-CHSH inequality is formulated in a manifestly BRST invariant way. The examples of the free four-dimensional Maxwell theory and the Abelian Higgs model are scrutinized. The inequality is probed by using BRST invariant squeezed states, allowing for large Bell-CHSH inequality violations, close to Tsirelson's bound. An illustrative comparison with the entangled state of two $1/2$ spin particles in Quantum Mechanics is provided.

  2 citations

• Symmetry-protected exceptional and nodal points in non-Hermitian systems

  Sharareh Sayyad, Marcus Stålhammar, Lukas Rødland, Flore K. Kunst

  SciPost Phys. 15, 200 (2023) · published 23 November 2023 | Toggle abstract · pdf

  One of the unique features of non-Hermitian (NH) systems is the appearance of NH degeneracies known as exceptional points (EPs). The extensively studied defective EPs occur when the Hamiltonian becomes non-diagonalizable. Aside from this degeneracy, we show that NH systems may host two further types of non-defective degeneracies, namely, non-defective EPs and ordinary (Hermitian) nodal points. The non-defective EPs manifest themselves by i) the diagonalizability of the NH Hamiltonian at these points and ii) the non-diagonalizability of the Hamiltonian along certain intersections of these points, resulting in instabilities in the Jordan decomposition when approaching the points from certain directions. We demonstrate that certain discrete symmetries, namely parity-time, parity-particle-hole, and pseudo-Hermitian symmetry, guarantee the occurrence of both defective and non-defective EPs. We extend this list of symmetries by including the NH time-reversal symmetry in two-band systems. Two-band and four-band models exemplify our findings. Through an example, we further reveal that ordinary nodal points may coexist with defective EPs in NH models when the above symmetries are relaxed.

  10 citations

• Constraining braneworlds with entanglement entropy

  Hao Geng, Andreas Karch, Carlos Perez-Pardavila, Lisa Randall, Marcos Riojas, Sanjit Shashi, Merna Youssef

  SciPost Phys. 15, 199 (2023) · published 21 November 2023 | Toggle abstract · pdf

  We propose swampland criteria for braneworlds viewed as effective field theories of defects coupled to semiclassical gravity. We do this by exploiting their holographic interpretation. We focus on general features of entanglement entropies and their holographic calculations. Entropies have to be positive. Furthermore, causality imposes certain constraints on the surfaces that are used holographically to compute them, most notably a property known as causal wedge inclusion. As a test case, we explicitly constrain the Dvali-Gabadadze-Porrati term as a second-order-in-derivatives correction to the Randall-Sundrum action. We conclude by discussing the implications of these criteria for the question on whether entanglement islands in theories with massless gravitons are possible in Karch-Randall braneworlds.

  10 citations

• Stress Tensor flows, birefringence in non-linear electrodynamics and supersymmetry

  Christian Ferko, Liam Smith, Gabriele Tartaglino-Mazzucchelli

  SciPost Phys. 15, 198 (2023) · published 21 November 2023 | Toggle abstract · pdf

  We identify the unique stress tensor deformation which preserves zero-birefringence conditions in non-linear electrodynamics, which is a $4d$ version of the $T\overline{T}$ operator. We study the flows driven by this operator in the three Lagrangian theories without birefringence - Born-Infeld, Plebanski, and reverse Born-Infeld - all of which admit ModMax-like generalizations using a root-$T\overline{T}$-like flow that we analyse in our paper. We demonstrate one way of making this root-$T\overline{T}$-like flow manifestly supersymmetric by writing the deforming operator in $\mathcal{N} = 1$ superspace and exhibit two examples of superspace flows. We present scalar analogues in $d = 2$ with similar properties as these theories of electrodynamics in $d = 4$. Surprisingly, the Plebanski-type theories are fixed points of the classical $T\overline{T}$-like flows, while the Born-Infeld-type examples satisfy new flow equations driven by relevant operators constructed from the stress tensor. Finally, we prove that any theory obtained from a classical stress-tensor-squared deformation of a conformal field theory gives rise to a related "subtracted" theory for which the stress-tensor-squared operator is a constant.

  8 citations

• No superconductivity in Pb$_9$Cu$_1$(PO$_4$)$_6$O found in orbital and spin fluctuation exchange calculations

  Niklas Witt, Liang Si, Jan M. Tomczak, Karsten Held, Tim O. Wehling

  SciPost Phys. 15, 197 (2023) · published 21 November 2023 | Toggle abstract · pdf

  Finding a material that turns superconducting under ambient conditions has been the goal of over a century of research, and recently Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O aka LK-99 has been put forward as a possible contestant. In this work, we study the possibility of electronically driven superconductivity in LK-99 also allowing for electron or hole doping. We use an ab initio derived two-band model of the Cu $e_g$ orbitals for which we determine interaction values from the constrained random phase approximation (cRPA). For this two-band model we perform calculations in the fluctuation exchange (FLEX) approach to assess the strength of orbital and spin fluctuations. We scan over a broad range of parameters and enforce no magnetic or orbital symmetry breaking. Even under optimized conditions for superconductivity, spin and orbital fluctuations turn out to be too weak for superconductivity anywhere near to room-temperature. We contrast this finding to non-self-consistent RPA, where it is possible to induce spin singlet d-wave superconductivity at $T_c$ ≥300K if the system is put close enough to a magnetic instability.

  7 citations

• Exploring the vortex phase diagram of Bogoliubov-de Gennes disordered superconductors

  Bo Fan (范波), Antonio Miguel Garcia Garcia

  SciPost Phys. 15, 196 (2023) · published 15 November 2023 | Toggle abstract · pdf

  We study the interplay of vortices and disorder in a two-dimensional disordered superconductor at zero temperature described by the Bogoliubov-de Gennes (BdG) self-consistent formalism for lattices of sizes up to 100×100 where the magnetic flux is introduced by the Peierls substitution. We model substantially larger lattice size than in previous approaches (≤36×36) which has allowed us to identify a rich phase diagram as a function of the magnetic flux and the disorder strength. For sufficiently weak disorder, and not too strong magnetic flux, we observe a slightly distorted Abrikosov triangular vortex lattice. An increase in the magnetic flux leads to an unexpected rectangular vortex lattice. A further increase in disorder, or flux, gradually destroys the lattice symmetry though strong vortex repulsion persists. An even stronger disorder leads to deformed single vortices with an inhomogeneous core. As the number of vortices increases, vortex overlap becomes more frequent. Finally, we show that global phase coherence is a feature of all these phases and that disorder enhances substantially the critical magnetic flux with respect to the clean limit with a maximum on the metallic side of the insulating transition.

  2 citations

• Monopole harmonics on $\mathbb{CP}^{n-1}$

  Dmitri Bykov, Andrei Smilga

  SciPost Phys. 15, 195 (2023) · published 14 November 2023 | Toggle abstract · pdf

  We find the spectra and eigenfunctions of both ordinary and supersymmetric quantum-mechanical models describing the motion of a charged particle over the $\mathbb{CP}^{n-1}$ manifold in the presence of a background monopole-like gauge field. The states form degenerate $SU(n)$ multiplets and their wave functions acquire a very simple form being expressed via homogeneous coordinates. Their relationship to multidimensional orthogonal polynomials of a special kind is discussed. By the well-known isomorphism between the twisted Dolbeault and Dirac complexes, our construction also gives the eigenfunctions and eigenvalues of the Dirac operator on complex projective spaces in a monopole background.

  2 citations

• Probing fractional statistics in quantum simulators of spin liquid Hamiltonians

  Shiyu Zhou, Maria Zelenayova, Oliver Hart, Claudio Chamon, Claudio Castelnovo

  SciPost Phys. 15, 194 (2023) · published 14 November 2023 | Toggle abstract · pdf

  Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realise and investigate topological quantum spin liquid phases. This new and exciting direction brings about important research questions on how to probe and determine the presence of such exotic, highly entangled phases in a noisy quantum environment. One of the most promising tools is investigating the behaviour of the topological excitations, and in particular their fractional statistics. In this work we put forward a generic route to achieve this, and we illustrate it in the specific case of $\mathbb{Z}_2$ topological spin liquids implemented with the aid of combinatorial gauge symmetry. We design a convenient architecture to study signatures of fractional statistics via quasiparticle interferometry, and we assess its robustness to diagonal and off-diagonal disorder, as well as to dephasing - effects that are generally pervasive in current quantum programmable devices. Interestingly, when turned on its head, our scheme provides a remarkably clear test of the "quantumness" of these devices, with robust signatures that crucially hinge on quantum coherence and quantum interference effects, and cannot be mimicked by classical stochastic processes.

  2 citations