Publications

Order by: publication date number of citations

• Topological holography: The example of the D2-D4 brane system

  Nafiz Ishtiaque, Seyed Faroogh Moosavian, Yehao Zhou

  SciPost Phys. 9, 017 (2020) · published 5 August 2020 | Toggle abstract · pdf

  We propose a toy model for holographic duality. The model is constructed by embedding a stack of $N$ D2-branes and $K$ D4-branes (with one dimensional intersection) in a 6D topological string theory. The world-volume theory on the D2-branes (resp. D4-branes) is 2D BF theory (resp. 4D Chern-Simons theory) with $\mathrm{GL}_N$ (resp. $\mathrm{GL}_K$) gauge group. We propose that in the large $N$ limit the BF theory on $\mathbb{R}^2$ is dual to the closed string theory on $\mathbb R^2 \times \mathbb R_+ \times S^3$ with the Chern-Simons defect on $\mathbb R \times \mathbb R_+ \times S^2$. As a check for the duality we compute the operator algebra in the BF theory, along the D2-D4 intersection -- the algebra is the Yangian of $\mathfrak{gl}_K$. We then compute the same algebra, in the guise of a scattering algebra, using Witten diagrams in the Chern-Simons theory. Our computations of the algebras are exact (valid at all loops). Finally, we propose a physical string theory construction of this duality using a D3-D5 brane configuration in type IIB -- using supersymmetric twist and $\Omega$-deformation.

  16 citations

• On four-point connectivities in the critical 2d Potts model

  Marco Picco, Sylvain Ribault, Raoul Santachiara

  SciPost Phys. 7, 044 (2019) · published 7 October 2019 | Toggle abstract · pdf

  We perform Monte-Carlo computations of four-point cluster connectivities in the critical 2d Potts model, for numbers of states $Q\in (0,4)$ that are not necessarily integer. We compare these connectivities to four-point functions in a CFT that interpolates between D-series minimal models. We find that 3 combinations of the 4 independent connectivities agree with CFT four-point functions, down to the $2$ to $4$ significant digits of our Monte-Carlo computations. However, we argue that the agreement is exact only in the special cases $Q=0, 3, 4$. We conjecture that the Potts model can be analytically continued to a double cover of the half-plane $\{\Re c <13\}$, where $c$ is the central charge of the Virasoro symmetry algebra.

  16 citations

• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I

  Jean Michel Maillet, Giuliano Niccoli, Baptiste Pezelier

  SciPost Phys. 2, 009 (2017) · published 28 February 2017 | Toggle abstract · pdf

  We study the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazhanov-Stroganov Lax operator. The results apply as well to the spectral analysis of the lattice sine-Gordon model with integrable open boundary conditions. This spectral analysis is developed by implementing the method of separation of variables (SoV). The transfer matrix spectrum (both eigenvalues and eigenstates) is completely characterized in terms of the set of solutions to a discrete system of polynomial equations in a given class of functions. Moreover, we prove an equivalent characterization as the set of solutions to a Baxter's like T-Q functional equation and rewrite the transfer matrix eigenstates in an algebraic Bethe ansatz form. In order to explain our method in a simple case, the present paper is restricted to representations containing one constraint on the boundary parameters and on the parameters of the Bazhanov-Stroganov Lax operator. In a next article, some more technical tools (like Baxter's gauge transformations) will be introduced to extend our approach to general integrable boundary conditions.

  16 citations

• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality

  Weicheng Ye, Meng Guo, Yin-Chen He, Chong Wang, Liujun Zou

  SciPost Phys. 13, 066 (2022) · published 26 September 2022 | Toggle abstract · pdf

  Lieb-Schultz-Mattis (LSM) theorems provide powerful constraints on the emergibility problem, i.e. whether a quantum phase or phase transition can emerge in a many-body system. We derive the topological partition functions that characterize the LSM constraints in spin systems with $G_s\times G_{int}$ symmetry, where $G_s$ is an arbitrary space group in one or two spatial dimensions, and $G_{int}$ is any internal symmetry whose projective representations are classified by $\mathbb{Z}_2^k$ with $k$ an integer. We then apply these results to study the emergibility of a class of exotic quantum critical states, including the well-known deconfined quantum critical point (DQCP), $U(1)$ Dirac spin liquid (DSL), and the recently proposed non-Lagrangian Stiefel liquid. These states can emerge as a consequence of the competition between a magnetic state and a non-magnetic state. We identify all possible realizations of these states on systems with $SO(3)\times \mathbb{Z}_2^T$ internal symmetry and either $p6m$ or $p4m$ lattice symmetry. Many interesting examples are discovered, including a DQCP adjacent to a ferromagnet, stable DSLs on square and honeycomb lattices, and a class of quantum critical spin-quadrupolar liquids of which the most relevant spinful fluctuations carry spin-$2$. In particular, there is a realization of spin-quadrupolar DSL that is beyond the usual parton construction. We further use our formalism to analyze the stability of these states under symmetry-breaking perturbations, such as spin-orbit coupling. As a concrete example, we find that a DSL can be stable in a recently proposed candidate material, NaYbO$_2$.

  16 citations

• Weak integrability breaking and level spacing distribution

  D. Szász-Schagrin, B. Pozsgay, G. Takács

  SciPost Phys. 11, 037 (2021) · published 23 August 2021 | Toggle abstract · pdf

  Recently it was suggested that certain perturbations of integrable spin chains lead to a weak breaking of integrability in the sense that integrability is preserved at the first order in the coupling. Here we examine this claim using level spacing distribution. We find that the volume dependent crossover between integrable and chaotic level spacing statistics which marks the onset of quantum chaotic behaviour, is markedly different for weak vs. strong breaking of integrability. In particular, for the gapless case we find that the crossover coupling as a function of the volume $L$ scales with a $1/L^2$ law for weak breaking as opposed to the $1/L^3$ law previously found for the strong case.

  16 citations

• On anomalies and gauging of U(1) non-invertible symmetries in 4d QED

  Avner Karasik

  SciPost Phys. 15, 002 (2023) · published 6 July 2023 | Toggle abstract · pdf

  In this work we propose a way to promote the anomalous axial $U(1)$ transformations to exact non-invertible $U(1)$ symmetries. We discuss the procedure of coupling the non-invertible symmetry to a (dynamical or background) gauge field. We show that as part of the gauging procedure, certain constraints are imposed to make the gauging consistent. The constraints emerge naturally from the form of the non-invertible $U(1)$ conserved current. In the case of dynamical gauging, this results in new type of gauge theories we call non-invertible gauge theories: These are gauge theories with additional constraints that cancel the would-be gauge anomalies. By coupling to background gauge fields, we can discuss 't-Hooft anomalies of non-invertible symmetries. We show in an example that the matching conditions hold but they are realized in an unconventional way. Turning on non-trivial background for the non-invertible gauge field changes the vacuum even when the symmetry is not broken and the background is very weak. The anomalies are then matched by the appearance of solitons in the new vacuum.

  16 citations

• The self-consistent quantum-electrostatic problem in strongly non-linear regime

  Pacome Armagnat, A. Lacerda-Santos, Benoit Rossignol, Christoph Groth, Xavier Waintal

  SciPost Phys. 7, 031 (2019) · published 11 September 2019 | Toggle abstract · pdf

  The self-consistent quantum-electrostatic (also known as Poisson-Schr\"odinger) problem is notoriously difficult in situations where the density of states varies rapidly with energy. At low temperatures, these fluctuations make the problem highly non-linear which renders iterative schemes deeply unstable. We present a stable algorithm that provides a solution to this problem with controlled accuracy. The technique is intrinsically convergent including in highly non-linear regimes. We illustrate our approach with (i) a calculation of the compressible and incompressible stripes in the integer quantum Hall regime and (ii) a calculation of the differential conductance of a quantum point contact geometry. Our technique provides a viable route for the predictive modeling of the transport properties of quantum nanoelectronics devices.

  16 citations

• A Generalized Construction of Calabi-Yau Models and Mirror Symmetry

  Per Berglund, Tristan Hubsch

  SciPost Phys. 4, 009 (2018) · published 20 February 2018 | Toggle abstract · pdf

  We extend the construction of Calabi-Yau manifolds to hypersurfaces in non-Fano toric varieties, requiring the use of certain Laurent defining polynomials, and explore the phases of the corresponding gauged linear sigma models. The associated non-reflexive and non-convex polytopes provide a generalization of Batyrev's original work, allowing us to construct novel pairs of mirror models. We showcase our proposal for this generalization by examining Calabi-Yau hypersurfaces in Hirzebruch n-folds, focusing on n=3,4 sequences, and outline the more general class of so-defined geometries.

  16 citations

• Topological lattice models with constant Berry curvature

  Daniel Varjas, Ahmed Abouelkomsan, Kang Yang, Emil J. Bergholtz

  SciPost Phys. 12, 118 (2022) · published 6 April 2022 | Toggle abstract · pdf

  Band geometry plays a substantial role in topological lattice models. The Berry curvature, which resembles the effect of magnetic field in reciprocal space, usually fluctuates throughout the Brillouin zone. Motivated by the analogy with Landau levels, constant Berry curvature has been suggested as an ideal condition for realizing fractional Chern insulators. Here we show that while the Berry curvature cannot be made constant in a topological two-band model, lattice models with three or more degrees of freedom per unit cell can support exactly constant Berry curvature. However, contrary to the intuitive expectation, we find that making the Berry curvature constant does not always improve the properties of fractional Chern insulator states. In fact, we show that an "ideal flatband" cannot have constant Berry curvature, equivalently, we show that the density algebra of Landau levels cannot be realised in any tight-binding lattice system.

  16 citations

• Coherence requirements for quantum communication from hybrid circuit dynamics

  Shane P. Kelly, Ulrich Poschinger, Ferdinand Schmidt-Kaler, Matthew P. A. Fisher, Jamir Marino

  SciPost Phys. 15, 250 (2023) · published 22 December 2023 | Toggle abstract · pdf

  The coherent superposition of quantum states is an important resource for quantum information processing which distinguishes quantum dynamics and information from their classical counterparts. In this article we determine the coherence requirements to communicate quantum information in a broad setting encompassing monitored quantum dynamics and quantum error correction codes. We determine these requirements by considering hybrid circuits that are generated by a quantum information game played between two opponents, Alice and Eve, who compete by applying unitaries and measurements on a fixed number of qubits. Alice applies unitaries in an attempt to maintain quantum channel capacity, while Eve applies measurements in an attempt to destroy it. By limiting the coherence generating or destroying operations available to each opponent, we determine Alice's coherence requirements. When Alice plays a random strategy aimed at mimicking generic monitored quantum dynamics, we discover a coherence-tuned phase transitions in entanglement and quantum channel capacity. We then derive a theorem giving the minimum coherence required by Alice in any successful strategy, and conclude by proving that coherence sets an upper bound on the code distance in any stabelizer quantum error correction code. Such bounds provide a rigorous quantification of the coherence resource requirements for quantum communication and error correction.

  16 citations