Publications

Order by: publication date number of citations

• Geodesic geometry of 2+1-D Dirac materials subject to artificial, quenched gravitational singularities

  Seth M. Davis, Matthew S. Foster

  SciPost Phys. 12, 204 (2022) · published 27 June 2022 | Toggle abstract · pdf

  The spatial modulation of the Fermi velocity for gapless Dirac electrons in quantum materials is mathematically equivalent to the problem of massless fermions on a certain class of curved spacetime manifolds. We study null geodesic lensing through these manifolds, which are dominated by curvature singularities, such as nematic singularity walls (where the Dirac cone flattens along one direction). Null geodesics lens across these walls, but do so by perfectly collimating to a local transit angle. Nevertheless, nematic walls can trap null geodesics into stable or metastable orbits characterized by repeated transits. We speculate about the role of induced one-dimensionality for such bound orbits in 2D dirty d-wave superconductivity.

  5 citations

• An ideal rapid-cycle Thouless pump

  Savvas Malikis, Vadim Cheianov

  SciPost Phys. 12, 203 (2022) · published 27 June 2022 | Toggle abstract · pdf

  Thouless pumping is a fundamental instance of quantized transport, which is topologically protected. Although its theoretical importance, the adiabaticity condition is an obstacle for further practical applications. Here, focusing on the Rice-Mele model, we provide a family of finite-frequency examples that ensure both the absence of excitations and the perfect quantization of the pumped charge at the end of each cycle. This family, which contains an adiabatic protocol as a limiting case, is obtained through a mapping onto the zero curvature representation of the Euclidean sinh-Gordon equation.

  3 citations

• Gauging U(1) symmetry in (2+1)d topological phases

  Meng Cheng, Chao-Ming Jian

  SciPost Phys. 12, 202 (2022) · published 27 June 2022 | Toggle abstract · pdf

  We study the gauging of a global U(1) symmetry in a gapped system in (2+1)d. The gauging procedure has been well-understood for a finite global symmetry group, which leads to a new gapped phase with emergent gauge structure and can be described algebraically using the mathematical framework of modular tensor category (MTC). We develop a categorical description of U(1) gauging in an MTC, taking into account the dynamics of U(1) gauge field absent in the finite group case. When the ungauged system has a non-zero Hall conductance, the gauged theory remains gapped and we determine the complete set of anyon data for the gauged theory. On the other hand, when the Hall conductance vanishes, we argue that gauging has the same effect of condensing a special Abelian anyon nucleated by inserting $2\pi$ U(1) flux. We apply our procedure to the SU(2)$_k$ MTCs and derive the full MTC data for the $\mathbb{Z}_k$ parafermion MTCs. We also discuss a dual U(1) symmetry that emerges after the original U(1) symmetry of an MTC is gauged.

  3 citations

• A constructive theory of the numerically accessible many-body localized to thermal crossover

  Philip J D Crowley, Anushya Chandran

  SciPost Phys. 12, 201 (2022) · published 24 June 2022 | Toggle abstract · pdf

  The many-body localised (MBL) to thermal crossover observed in exact diagonalisation studies remains poorly understood as the accessible system sizes are too small to be in an asymptotic scaling regime. We develop a model of the crossover in short 1D chains in which the MBL phase is destabilised by the formation of many-body resonances. The model reproduces several properties of the numerically observed crossover, including an apparent correlation length exponent $\nu=1$, exponential growth of the Thouless time with disorder strength, linear drift of the critical disorder strength with system size, scale-free resonances, apparent $1/\omega$ dependence of disorder-averaged spectral functions, and sub-thermal entanglement entropy of small subsystems. In the crossover, resonances induced by a local perturbation are rare at numerically accessible system sizes $L$ which are smaller than a \emph{resonance length} $\lambda$. For $L \gg \sqrt{\lambda}$ (in lattice units), resonances typically overlap, and this model does not describe the asymptotic transition. The model further reproduces controversial numerical observations which Refs. [Suntajs et al 2019, Sels & Polkovnikov 2020] claimed to be inconsistent with MBL. We thus argue that the numerics to date is consistent with a MBL phase in the thermodynamic limit.

  46 citations

• On the dynamic distinguishability of nodal quasi-particles in overdoped cuprates

  Kamran Behnia

  SciPost Phys. 12, 200 (2022) · published 24 June 2022 | Toggle abstract · pdf

  La$_{1.67}$Sr$_{0.33}$CuO$_4$ is not a superconductor and its resistivity follows a purely T$^2$ temperature dependence at very low temperatures. La$_{1.71}$Sr$_{0.29}$CuO$_4$, on the other hand, has a superconducting ground state together with a T-Linear term in its resistivity. The concomitant emergence of these two features below a critical doping is mystifying. Here, I notice that the electron-electron collision rate in the Fermi liquid above the doping threshold is unusually large. The scattering time of nodal quasi-particles expressed in a dimensionless parameter $\zeta$ is very close to what has been found in liquid $^3$He at its melting pressure. In the latter case, fermionic particles become dynamically distinguishable by excess of interaction. Ceasing to be dynamically indistinguishable, nodal electrons will be excluded from the Fermi sea. Such non-degenerate carriers will then scatter the degenerate ones within a phase space growing linearly with temperature.

  3 citations

• Josephson junctions of topological nodal superconductors

  Ranjani Seshadri, Maxim Khodas, Dganit Meidan

  SciPost Phys. 12, 197 (2022) · published 23 June 2022 | Toggle abstract · pdf

  Transition metal dichalcogenides (TMDs) offer a unique platform to study unconventional superconductivity, owing to the presence of strong spin-orbit coupling and a remarkable stability to an in-plane magnetic field. A recent study found that when an in-plane field applied to a superconducting monolayer TMD is increased beyond the Pauli critical limit, a quantum phase transition occurs into a topological nodal superconducting phase which hosts Majorana flat bands. We study the current-phase relation of this nodal superconductor in a Josephson junction geometry. We find that the nodal superconductivity is associated with an energy-phase relation that depends on the momentum transverse to the current direction, with a $4\pi$ periodicity in between pairs of nodal points. We interpret this response as a result of a series of quantum phase transitions, driven by the transverse momentum, which separate a topological trivial phase and two distinct topologically non-trivial phases characterized by different winding invariants. This analysis sheds light on the stability of the Majorana flat bands to symmetry-breaking perturbations.

  3 citations

• Edge physics at the deconfined transition between a quantum spin Hall insulator and a superconductor

  Ruochen Ma, Liujun Zou, Chong Wang

  SciPost Phys. 12, 196 (2022) · published 14 June 2022 | Toggle abstract · pdf

  We study the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary. We calculate various edge properties in an $N\to\infty$ limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as "fractional" degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the quantum spin Hall state but with the full $SU(2)$ spin rotation symmetry, which cannot be realized if the bulk is gapped.

  7 citations

• Entanglement entropy in quantum spin chains with broken parity number symmetry

  Arash Jafarizadeh, M. A. Rajabpour

  SciPost Phys. 12, 195 (2022) · published 14 June 2022 | Toggle abstract · pdf

  Consider a generic quantum spin chain that can be mapped to free quadratic fermions via Jordan-Wigner (JW) transformation. In the presence of arbitrary boundary magnetic fields, this Hamiltonian is no longer a quadratic Hamiltonian after JW transformation. Using ancillary sites and enlarging the Hamiltonian we first introduce a bigger quadratic Hamiltonian. Then we diagonalize this enlarged Hamiltonian in its most generic form and show that all the states are degenerate because of the presence of a zero mode. The eigenstates of the original spin chain with boundary magnetic fields can be derived after appropriate projection. We study in-depth the properties of the eigenstates of the enlarged Hamiltonian. In particular, we find: 1) the eigenstates in configuration bases, 2) calculate all the correlation functions, 3) find the reduced density matrices, 4) calculate the entanglement entropy. We show that the generic eigenstate of the enlarged Hamiltonian (including the eigenstates of the original spin chain) breaks the parity number symmetry and consequently one needs to take care of some technicalities regarding the calculation of the reduced density matrix and entanglement entropy. Interestingly we show that the entanglement structure of these eigenstates is quite universal and independent of the Hamiltonian. We support our results by applying them to a couple of examples.

  4 citations

• Rényi entropies and negative central charges in non-Hermitian quantum systems

  Yi-Ting Tu, Yu-Chin Tzeng, Po-Yao Chang

  SciPost Phys. 12, 194 (2022) · published 13 June 2022 | Toggle abstract · pdf

  Quantum entanglement is one essential element to characterize many-body quantum systems. However, the entanglement measures are mostly discussed in Hermitian systems. Here, we propose a natural extension of entanglement and R\'enyi entropies to non-Hermitian quantum systems. There have been other proposals for the computation of these quantities, which are distinct from what is proposed in the current paper. We demonstrate the proposed entanglement quantities which are referred to as generic entanglement and R\'enyi entropies. These quantities capture the desired entanglement properties in non-Hermitian critical systems, where the low-energy properties are governed by the non-unitary conformal field theories (CFTs). We find excellent agreement between the numerical extrapolation of the negative central charges from the generic entanglement/R\'enyi entropy and the non-unitary CFT prediction. Furthermore, we apply the generic entanglement/R\'enyi entropy to symmetry-protected topological phases with non-Hermitian perturbations. We find the generic $n$-th R\'enyi entropy captures the expected entanglement property, whereas the traditional R\'enyi entropy can exhibit unnatural singularities due to its improper definition.

  18 citations

• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap

  Jaychandran Padayasi, Abijith Krishnan, Max A. Metlitski, Ilya A. Gruzberg, Marco Meineri

  SciPost Phys. 12, 190 (2022) · published 9 June 2022 | Toggle abstract · pdf

  This paper studies the critical behavior of the 3d classical $\mathrm{O}(N)$ model with a boundary. Recently, one of us established that upon treating $N$ as a continuous variable, there exists a critical value $N_c > 2$ such that for $2 \leq N < N_c$ the model exhibits a new extraordinary-log boundary universality class, if the symmetry preserving interactions on the boundary are enhanced. $N_c$ is determined by a ratio of universal amplitudes in the normal universality class, where instead a symmetry breaking field is applied on the boundary. We study the normal universality class using the numerical conformal bootstrap. We find truncated solutions to the crossing equation that indicate $N_c \approx 5$. Additionally, we use semi-definite programming to place rigorous bounds on the boundary CFT data of interest to conclude that $N_c > 3$, under a certain positivity assumption which we check in various perturbative limits.

  42 citations