Publications

Order by: publication date number of 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.

  20 citations

• Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions

  Sthitadhi Roy, David E. Logan

  SciPost Phys. 7, 042 (2019) · published 3 October 2019 | Toggle abstract · pdf

  Many-body localisation is studied in a disordered quantum spin-1/2 chain with long-ranged power-law interactions, and distinct power-law exponents for interactions between longitudinal and transverse spin components. Using a self-consistent mean-field theory centring on the local propagator in Fock space and its associated self-energy, a localisation phase diagram is obtained as a function of the power-law exponents and the disorder strength of the random fields acting on longitudinal spin-components. Analytical results are corroborated using the well-studied and complementary numerical diagnostics of level statistics, entanglement entropy, and participation entropy, obtained via exact diagonalisation. We find that increasing the range of interactions between transverse spin components hinders localisation and enhances the critical disorder strength. In marked contrast, increasing the interaction range between longitudinal spin components is found to enhance localisation and lower the critical disorder.

  40 citations

• Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice

  Didier Poilblanc, Matthieu Mambrini, Sylvain Capponi

  SciPost Phys. 7, 041 (2019) · published 2 October 2019 | Toggle abstract · pdf

  We consider a family of SU(2)-symmetric Projected Entangled Paired States (PEPS) on the square lattice, defining colored-Resonating Valence Bond (RVB) states, to describe the quantum disordered phase of the $J_1-J_2$ frustrated Heisenberg model.For $J_2/J_1\sim 0.55$ we show the emergence of critical (algebraic) dimer-dimer correlations -- typical of Rokhsar-Kivelson (RK) points of quantum dimer models on bipartite lattices -- while, simultaneously, the spin-spin correlation length remains short. Our findings are consistent with a spin liquid or a weak Valence Bond Crystal in the neighborhood of an RK point.

  12 citations

• Logarithmic correlation functions for critical dense polymers on the cylinder

  Alexi Morin-Duchesne, Jesper Lykke Jacobsen

  SciPost Phys. 7, 040 (2019) · published 30 September 2019 | Toggle abstract · pdf

  We compute lattice correlation functions for the model of critical dense polymers on a semi-infinite cylinder of perimeter $n$. In the lattice loop model, contractible loops have a vanishing fugacity whereas non-contractible loops have a fugacity $\alpha \in (0,\infty)$. These correlators are defined as ratios $Z(x)/Z_0$ of partition functions, where $Z_0$ is a reference partition function wherein only simple half-arcs are attached to the boundary of the cylinder. For $Z(x)$, the boundary of the cylinder is also decorated with simple half-arcs, but it also has two special positions $1$ and $x$ where the boundary condition is different. We investigate two such kinds of boundary conditions: (i) there is a single node at each of these points where a long arc is attached, and (ii) there are pairs of adjacent nodes at these points where two long arcs are attached. We find explicit expressions for these correlators for finite $n$ using the representation of the enlarged periodic Temperley-Lieb algebra in the XX spin chain. The resulting asymptotics as $n\to \infty$ are expressed as simple integrals that depend on the scaling parameter $\tau = \frac {x-1} n \in (0,1)$. For small $\tau$, the leading behaviours are proportional to $\tau^{1/4}$, $\tau^{1/4}\log \tau$, $\log \tau$ and $\log^2 \tau$. We interpret the lattice results in terms of ratios of conformal correlation functions. We assume that the corresponding boundary changing fields are highest weight states in irreducible, Kac or staggered Virasoro modules, with central charge $c=-2$ and conformal dimensions $\Delta = -\frac18$ or $\Delta = 0$. With these assumptions, we obtain differential equations of order two and three satisfied by the conformal correlation functions, solve these equations in terms of hypergeometric functions, and find a perfect agreement with the lattice results. We use the lattice results to compute structure constants and ratios thereof which appear in the operator product expansions of the boundary condition changing fields. The fusion of these fields is found to be non-abelian.

  1 citation

• Supercurrent-induced Majorana bound states in a planar geometry

  André Melo, Sebastian Rubbert, Anton R. Akhmerov

  SciPost Phys. 7, 039 (2019) · published 27 September 2019 | Toggle abstract · pdf

  We propose a new setup for creating Majorana bound states in a two-dimensional electron gas Josephson junction. Our proposal relies exclusively on a supercurrent parallel to the junction as a mechanism of breaking time-reversal symmetry. We show that combined with spin-orbit coupling, supercurrents induce a Zeeman-like spin splitting. Further, we identify a new conserved quantity---charge-momentum parity---that prevents the opening of the topological gap by the supercurrent in a straight Josephson junction. We propose breaking this conservation law by adding a third superconductor, introducing a periodic potential, or making the junction zigzag-shaped. By comparing the topological phase diagrams and practical limitations of these systems we identify the zigzag-shaped junction as the most promising option.

  28 citations

• Twisted and untwisted negativity spectrum of free fermions

  Hassan Shapourian, Paola Ruggiero, Shinsei Ryu, Pasquale Calabrese

  SciPost Phys. 7, 037 (2019) · published 25 September 2019 | Toggle abstract · pdf

  A basic diagnostic of entanglement in mixed quantum states is known as the positive partial transpose (PT) criterion. Such criterion is based on the observation that the spectrum of the partially transposed density matrix of an entangled state contains negative eigenvalues, in turn, used to define an entanglement measure called the logarithmic negativity. Despite the great success of logarithmic negativity in characterizing bosonic many-body systems, generalizing the operation of PT to fermionic systems remained a technical challenge until recently when a more natural definition of PT for fermions that accounts for the Fermi statistics has been put forward. In this paper, we study the many-body spectrum of the reduced density matrix of two adjacent intervals for one-dimensional free fermions after applying the fermionic PT. We show that in general there is a freedom in the definition of such operation which leads to two different definitions of PT: the resulting density matrix is Hermitian in one case, while it becomes pseudo-Hermitian in the other case. Using the path-integral formalism, we analytically compute the leading order term of the moments in both cases and derive the distribution of the corresponding eigenvalues over the complex plane. We further verify our analytical findings by checking them against numerical lattice calculations.

  67 citations

• Curvature induced magnonic crystal in nanowires

  Anastasiia Korniienko, Volodymyr P. Kravchuk, Oleksandr V. Pylypovskyi, Denis D. Sheka, Jeroen van den Brink, Yuri Gaididei

  SciPost Phys. 7, 035 (2019) · published 20 September 2019 | Toggle abstract · pdf

  A new type of magnonic crystals, curvature induced ones, is realized in ferromagnetic nanowires with periodically deformed shape. A magnon band structure of such crystal is fully determined by its curvature: the developed theory is well confirmed by simulations. An application to nanoscale spintronic devices with the geometrically tunable parameters is proposed, namely, to filter elements.

  14 citations

• The equilibrium landscape of the Heisenberg spin chain

  Enej Ilievski, Eoin Quinn

  SciPost Phys. 7, 033 (2019) · published 13 September 2019 | Toggle abstract · pdf

  We characterise the equilibrium landscape, the entire manifold of local equilibrium states, of an interacting integrable quantum model. Focusing on the isotropic Heisenberg spin chain, we describe in full generality two complementary frameworks for addressing equilibrium ensembles: the functional integral Thermodynamic Bethe Ansatz approach, and the lattice regularisation transfer matrix approach. We demonstrate the equivalence between the two, and in doing so clarify several subtle features of generic equilibrium states. In particular we explain the breakdown of the canonical Y-system, which reflects a hidden structure in the parametrisation of equilibrium ensembles.

  10 citations

• Invariants of winding-numbers and steric obstruction in dynamics of flux lines

  Olivier Cépas, Peter M. Akhmetiev

  SciPost Phys. 7, 032 (2019) · published 12 September 2019 | Toggle abstract · pdf

  We classify the sectors of configurations that result from the dynamics of 2d crossing flux lines, which are the simplest degrees of freedom of the 3-coloring lattice model. We show that the dynamical obstruction is the consequence of two effects: (i) conservation laws described by a set of invariants that are polynomials of the winding numbers of the loop configuration, (ii) steric obstruction that prevents paths between configurations, for lack of free space. We argue that the invariants fully classify the configurations in five, chiral and achiral, sectors and no further obstruction in the limit of low-winding numbers.

  1 citation

• 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.

  20 citations