Publications

Order by: publication date number of citations

• Ground state topology of a four-terminal superconducting double quantum dot

  Lev Teshler, Hannes Weisbrich, Jonathan Sturm, Raffael L. Klees, Gianluca Rastelli, Wolfgang Belzig

  SciPost Phys. 15, 214 (2023) · published 29 November 2023 | Toggle abstract · pdf

  In recent years, various classes of systems were proposed to realize topological states of matter. One of them are multiterminal Josephson junctions where topological Andreev bound states are constructed in the synthetic space of superconducting phases. Crucially, the topology in these systems results in a quantized transconductance between two of its terminals comparable to the quantum Hall effect. In this work, we study a double quantum dot with four superconducting terminals and show that it has an experimentally accessible topological regime in which the non-trivial topology can be measured. We also include Coulomb repulsion between electrons which is usually present in experiments and show how the topological region can be maximized in parameter space.

  8 citations

• A bound on thermal relativistic correlators at large spacelike momenta

  Souvik Banerjee, Kyriakos Papadodimas, Suvrat Raju, Prasant Samantray, Pushkal Shrivastava

  SciPost Phys. 8, 064 (2020) · published 20 April 2020 | Toggle abstract · pdf

  We consider thermal Wightman correlators in a relativistic quantum field theory in the limit where the spatial momenta of the insertions become large while their frequencies stay fixed. We show that, in this limit, the size of these correlators is bounded by $e^{-\beta R}$, where $R$ is the radius of the smallest sphere that contains the polygon formed by the momenta. We show that perturbative quantum field theories can saturate this bound through suitably high-order loop diagrams. We also consider holographic theories in $d$-spacetime dimensions, where we show that the leading two-point function of generalized free-fields saturates the bound in $d = 2$ and is {\em below} the bound for $d > 2$. We briefly discuss interactions in holographic theories and conclude with a discussion of several open problems.

  8 citations

• Harmonic chain far from equilibrium: Single-file diffusion, long-range order, and hyperuniformity

  Harukuni Ikeda

  SciPost Phys. 17, 103 (2024) · published 3 October 2024 | Toggle abstract · pdf

  In one dimension, particles can not bypass each other. As a consequence, the mean-squared displacement (MSD) in equilibrium shows sub-diffusion $MSD(t)\sim t^{1/2}$, instead of normal diffusion $MSD(t)\sim t$. This phenomenon is the so-called single-file diffusion. Here, we investigate how the above equilibrium behaviors are modified far from equilibrium. In particular, we want to uncover what kind of non-equilibrium driving force can suppress diffusion and achieve the long-range crystalline order in one dimension, which is prohibited by the Mermin-Wagner theorem in equilibrium. For that purpose, we investigate the harmonic chain driven by the following four types of driving forces that do not satisfy the detailed balance: (i) temporally correlated noise with the noise spectrum $D(\omega)\sim \omega^{-2\theta}$, (ii) conserving noise, (iii) periodic driving force, and (iv) periodic deformations of particles. For the driving force (i) with $\theta>-1/4$, we observe $MSD(t)\sim t^{1/2+2\theta}$ for large $t$. On the other hand, for the driving forces (i) with $\theta<-1/4$ and (ii)-(iv), MSD remains finite. As a consequence, the harmonic chain exhibits the crystalline order even in one dimension. Furthermore, the density fluctuations of the model are highly suppressed in a large scale in the crystal phase. This phenomenon is known as hyperuniformity. We discuss that hyperuniformity of the noise fluctuations themselves is the relevant mechanism to stabilize the long-range crystalline order in one dimension and yield hyperuniformity of the density fluctuations.

  8 citations

• Out of equilibrium many-body expansion dynamics of strongly interacting bosons

  Rhombik Roy, Barnali Chakrabarti, Arnaldo Gammal

  SciPost Phys. Core 6, 073 (2023) · published 3 November 2023 | Toggle abstract · pdf

  We solve the Schrödinger equation from first principles to investigate the many-body effects in the expansion dynamics of one-dimensional repulsively interacting bosons released from a harmonic trap. We utilize the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) to solve the many-body Schrödinger equation at high level of accuracy. The MCTDHB basis sets are explicitly time-dependent and optimised by variational principle. We probe the expansion dynamics by three key measures; time evolution of one-, two- and three-body densities. We observe when the mean-field theory results to unimodal expansion, the many-body calculation exhibits trimodal expansion dynamics. The many-body features how the initially fragmented bosons independently spreads out with time whereas the mean-field pictures the expansion of the whole cloud. We also present the three different time scale of dynamics of the inner core, outer core and the cloud as a whole. We analyze the key role played by the dynamical fragmentation during expansion. A Strong evidence of the many-body effects is presented in the dynamics of two- and three-body densities which exhibit correlation hole and pronounced delocalization effect.

  8 citations

• Introduction to Hamiltonian formulation of general relativity and homogeneous cosmologies

  Rishabh Jha

  SciPost Phys. Lect. Notes 73 (2023) · published 11 August 2023 | Toggle abstract · pdf

  We give a pedagogical introduction to the Hamiltonian formalism of general relativity at an advanced undergraduate and graduate levels. After covering the mathematical pre-requisites as well as the 3+1-decomposition of spacetime, we proceed to discuss the Arnowitt-Deser-Misner (ADM) formalism (a Hamiltonian approach) of general relativity. Then we proceed to give a brief but self-contained introduction to homogeneous (but not necessarily isotropic) universes and discuss the associated Bianchi classification. We first study their dynamics in the Lagrangian formulation, followed by the Hamiltonian formulation to show the equivalence of both approaches. We present a variety of examples to illustrate the ADM formalism: (i) free & massless scalar field coupled to homogeneous (in particular, Bianchi IX) universe, (ii) scalar field with a potential term coupled to Bianchi IX universe, (iii) electromagnetic field coupled to gravity in general, and (iv) electromagnetic field coupled to Bianchi IX universe.

  8 citations

• Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator

  Xue-Yang Song, Ya-Hui Zhang

  SciPost Phys. 15, 215 (2023) · published 29 November 2023 | Toggle abstract · pdf

  We propose bi-critical and tri-critical theories between chiral spin liquid (CSL), topological superconductor (SC) and charge density wave (CDW) ordered Chern insulator with Chern number $C=2$ on square, triangular and Kagome lattices. The three CDW order parameters form a manifold of $S^2$ or $S^1$ depending on whether there is easy-plane anisotropy. The skyrmion defect of the CDW order carries physical charge $2e$ and its condensation leads to a topological superconductor. The CDW-SC transitions are in the same universality classes as the celebrated deconfined quantum critical points (DQCP) between Neel order and valence bond solid order on square lattice. Both SC and CDW order can be accessed from the CSL phase through a continuous phase transition. At the CSL-SC transition, there is still CDW order fluctuations although CDW is absent in both sides. We propose three different theories for the CSL-SC transition (and CSL to easy-plane CDW transition): a $U(1)$ theory with two bosons, a $U(1)$ theory with two Dirac fermions, and an $SU(2)$ theory with two bosons. Our construction offers a derivation of the duality between these three theories as well as a promising physical realization. The $SU(2)$ theory offers a unified framework for a series of fixed points with explicit $SO(5), O(4)$ or $SO(3)× O(2)$ symmetry. There is also a transparent duality transformation mapping SC order to easy-plane CDW order. The CSL-SC-CDW tri-critical points are invariant under this duality mapping and have an enlarged $SO(5)$ or $O(4)$ symmetry. The DQCPs between CDW and SC inherit the enlarged symmetry, emergent anomaly, and self-duality from the tri-critical point. Our analysis unifies the well-studied DQCP between symmetry breaking phases into a larger framework where they are proximate to a topologically ordered phase. Experimentally the theory demonstrates the possibility of a rich phase diagram and criticality through closing the Mott gap of a quantum spin liquid with projective symmetry group.

  7 citations

• Topological field theory approach to intermediate statistics

  Ward L. Vleeshouwers, Vladimir Gritsev

  SciPost Phys. 10, 146 (2021) · published 16 June 2021 | Toggle abstract · pdf

  Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are characterized by the spectral form factor (SFF). Here, we calculate the SFF of unitary matrix ensembles of infinite order with the weight function satisfying the assumptions of Szegö’s limit theorem. We then consider a parameter-dependent critical ensemble which has intermediate statistics characteristic of ergodic-to-nonergodic transitions such as the Anderson localization transition. This same ensemble is the matrix model of $U(N)$ Chern-Simons theory on $S^3$ , and the SFF of this ensemble is proportional to the HOMFLY invariant of (2n,2)-torus links with one component in the fundamental and one in the antifundamental representation. This is one example of a large class of ensembles with intermediate statistics arising from topological field and string theories. Indeed, the absence of a local order parameter suggests that it is natural to characterize ergodic-to-nonergodic transitions using topological tools, such as we have done here.

  7 citations

• The Conformal Spectrum of Non-Abelian Anyons

  Nima Doroud, David Tong, Carl Turner

  SciPost Phys. 4, 022 (2018) · published 30 April 2018 | Toggle abstract · pdf

  We study the spectrum of multiple non-Abelian anyons in a harmonic trap. The system is described by Chern-Simons theory, coupled to either bosonic or fermionic non-relativistic matter, and has an SO(2,1) conformal invariance. We describe a number of special properties of the spectrum, focussing on a class of protected states whose energies are dictated by their angular momentum. We show that the angular momentum of a bound state of non-Abelian anyons is determined by the quadratic Casimirs of their constituents.

  7 citations

• Hypercharge quantisation and Fermat's last theorem

  Nakarin Lohitsiri, David Tong

  SciPost Phys. 8, 009 (2020) · published 23 January 2020 | Toggle abstract · pdf

  What values of the Standard Model hypercharges result in a mathematically consistent quantum field theory? We show that the constraints imposed by the lack of gauge anomalies can be recast as the equation x^3 + y^3 = z^3. If hypercharge is quantised, then x, y and z must be integers. The trivial (and only) solutions, with x=0 or y=0, reproduce the hypercharge assignments seen in Nature. This argument does not rely on the mixed gauge-gravitational anomaly, which is automatically vanishing if hypercharge is quantised and the gauge anomalies vanish.

  7 citations

• Confined vs. extended Dirac surface states in topological crystalline insulator nanowires

  Roni Majlin Skiff, Fernando de Juan, Raquel Queiroz, Subramanian Mathimalar, Haim Beidenkopf, Roni Ilan

  SciPost Phys. Core 6, 011 (2023) · published 13 March 2023 | Toggle abstract · pdf

  Confining two dimensional Dirac fermions on the surface of topological insulators has remained an outstanding conceptual challenge. Here we show that Dirac fermion confinement is achievable in topological crystalline insulators (TCI), which host multiple surface Dirac cones depending on the surface termination and the symmetries it preserves. This confinement is most dramatically reflected in the flux dependence of these Dirac states in the nanowire geometry, where different facets connect to form a closed surface. Using SnTe as a case study, we show how wires with all four facets of the $\langle 100 \rangle$ type display novel Aharonov-Bohm oscillations, while nanowires with the four facets of the $\langle 110 \rangle$ type such oscillations are absent due to strong confinement of the Dirac states to each facet separately. Our results place TCI nanowires as a versatile platform for confining and manipulating Dirac surface states.

  7 citations