Session S56: Topology and Correlations

Optical Evidence of an Enhanced Electronic Effective Mass in the Anomalous Pb1-xTlxTe Superconductor

The narrow band-gap semiconductor PbTe exhibits a number of striking properties upon thallium (Tl)-doping, including the onset of superconductivity at temperatures T_c which are substantially higher than for materials with equivalent charge carrier concentration. Here, we provide a thorough optical investigation of Pb_1-xTl_xTe over a very broad spectral range and contrast its normal-state, complete excitation spectrum with the optical response of the non-superconducting analog Na-doped PbTe [1]. We capture the relevant energy scales shaping their electronic structure and uncover the formation of an impurity band upon doping with Tl, which evolves into a resonant state for large doping. This implies a large density of states and an enhancement of the optical effective mass m*/m_e of the itinerant charge carriers, which is stronger for Tl- than for Na-doping. Since the enhancement of m*/m_e particularly occurs upon crossing a critical concentration x_c in Tl-doped PbTe for which T_c≠ 0, we advance its relevance for the onset of superconductivity.
[1] A. Pal et al., Phys. Rev. Materials 3, 054801 (2019).   

Weyl-Kondo semimetal: controlling the nodes via magnetic field

In the effort to study topological metals in strongly-correlated settings, a Weyl-Kondo semimetal (WKSM) has been concurrently discovered in theoretical¹ and experimental^2,3 studies. This time-reversal-invariant state appears in a non-centrosymmetric Kondo lattice model. The theoretical and experimental signatures of the WKSM phase, include correlations-enhanced specific heat C=Γ T³ and a giant topological Hall response from the Kondo-driven Weyl nodes being pinned near the Fermi energy. Recently, high magnetic field experiments revealed a two-stage quantum phase transition, including a topological transition from the WKSM to a Kondo insulator.⁴ To connect with these experiments, we studied an Anderson lattice model with terms that break both time reversal and inversion symmetries.⁵ Tuning these terms controls the position and number of Weyl nodes in the Brillouin zone, and several topologically distinct phases emerge in this model.

¹H.-H. Lai, S. E. Grefe, S. Paschen, and Q. Si, PNAS 115, 93 2018
²S. Dzsaber et al., PRL 118, 246601 2017
³S. Dzsaber et al., arXiv:1811.02819 2018
⁴S. Dzsaber et al., arXiv:1906.01182 2019
⁵S. E. Grefe, H.-H. Lai, S. Paschen, and Q. Si, Weyl-Kondo semimetal: towards control of Weyl nodes 2019   

Quasiparticles as Detector of Topological Quantum Phase Transitions

Phases and phase transitions provide an important framework to understand the physics of strongly correlated quantum many-body systems. Topologically ordered phases of matter are particularly challenging in this context, because they are characterized by long-range entanglement and go beyond the Landau-Ginzburg theory. A few tools have been developed to study topological phase transitions, but the needed computations are generally demanding, they typically require the system to have particular boundary conditions, and they often provide only partial information. There is hence a high demand for developing further probes. Here, we propose to use the study of quasiparticle properties to detect phase transitions. Topologically ordered states support anyonic quasiparticles with special braiding properties and fractional charge. Being able to generate a given type of anyons in a system is a direct method to detect the topology, and the approach is independent from the choice of boundary conditions. We provide three examples, and for all of them we find that it is sufficient to study the anyon charge to detect the phase transition point. This makes the method numerically cheap.   

Higher-form symmetry perspective on fracton phases

Higher form symmetry provides a framework to understand some aspects of topologically ordered phases. Motivated by this, we study the role that higher form symmetry plays in the context of fracton phases. We introduce the notion of a non-faithful higher form symmetry and describe how fractons can arise via condensation of objects charged under such a symmetry. Finally we describe how such a non-faithful higher form symmetry can arise as a quotient of an ordinary higher-form symmetry via gauging certain subgroups.   

Local and Non-local correlation effects in topological quantum phase transitions

The fate of quantum phase transition among different topological states in presence of strong interaction is of primary interest in condensed matter.
We study the effects of electronic interactions at the local and non-local level in a paradigmatic model for topological insulator in two dimensions.
In the non-interacting regime topological transitions occurs via the continuous closing the energy gap.
Using Dynamical Mean-Field Theory and various cluster extensions (Cluster-DMFT, Variational Cluster Approximation, etc.), we show how short-range correlation effects are responsible for the breakdown of the continuous topological transition in favour of a first-order one. The discontinuous transition occurs without the celebrated closing of the energy gap, yet without the breaking of the symmetries which protect the topological state.

References:
A. Amaricci, J. C. Budich, M. Capone, B. Trauzettel, and G. Sangiovanni, Phys. Rev. Lett. 114, 185701 (2015)
A. Amaricci, J. C. Budich, M. Capone, B. Trauzettel, and G. Sangiovanni, Phys. Rev. B 93, 235112 (2016)
L. Crippa, A. Amaricci, N. Wagner, G. Sangiovanni, J. C. Budich, and M. Capone,arXiv:1904.11836 (2019)   

Anomalous localization at the boundary of an interacting topological insulator

The boundary of a topological insulator (TI) hosts an anomaly restricting its possible phases: e.g. 3D strong and weak TIs maintain surface conductivity at any disorder if symmetry is preserved on-average, at least when electron interactions on the surface are weak. However the interplay of strong interactions and disorder with the boundary anomaly has not been well studied theoretically. Here we present our results on this combination, for the edge of a 2D TI and the surface of a 3D weak TI, showing how it can lead to an "Anomalous Many Body Localized" (AMBL) phase that preserves the anomaly. We discuss its anomaly manifestation, predictions for experimental observations, and theoretical consequences for understanding 3D TIs and anomaly restrictions.   

Interaction effects on centrosymmetric Bogoliubov Fermi surfaces

Exotic quantum phases including topological insulators/semi-metals and non-Fermi liquids may be realized by quantum states with total angular momentum j=3/2 as manifested in HgTe and pyrochlore iridates. Recently, an exotic superconducting state with a finite density of zero energy Bogoliubov quasiparticles, Bogoliubov Fermi-surface, was also proposed in a centrosymmetric j=3/2 system with a Z2 topological invariant. We consider interaction effects of the Bogoliubov Fermi surfaces by using standard renormalization group and mean-field theory and discuss the implication of inversion symmetry breaking. Possible applications of our theory to iron based superconductors and heavy fermion systems including FeSe are also discussed   

Twisted dualities and the 2d Majorana checkerboard

Large ensembles of bound Majorana modes can form their own strongly-interacting phases of matter. For example, a square lattice of Majoranas coupled purely by four-fermion plaquette terms may be the effective description for the vortex lattice on the surface of certain 3d topological insulators. This talk leverages recently formulated exact dualities to derive novel representations of such a 2d Majorana checkerboard. Some connections to quantum cellular automata (QCA) and subsystem symmetry protected topological order (SSPT) are also discussed.   

Universal SPT invariants using swap operators

We will describe many-body topological invariants/order parameters for SPT phases that involve acting with symmetry operators and a swap operator. To do so, we use the universal notion of distinguishing between different phases of matter: phases are equivalence classes defined in the thermodynamic limit by (i) adiabatic continuity, and (ii) adding trivial degrees of freedom. In the process, we will also formulate gauge-invariant versions of these order parameters. Since our arguments for the universality of such many-body invariants do not depend on the spatial dimension we are working in, this discussion can help serve as a basis for generalizations to higher spatial dimensions. We will also show how to picture the invariant by putting the system on a spacetime manifold and by thinking in terms of TQFT partition functions.   

Exceptional-torus in strongly correlated nodal-line semimetals with many-body chiral symmetry

Recent studies have revealed a new type of topological phase described by a non-Hermitian (NH) Hamiltonian. In equilibrium systems, if we describe the energy spectrum of quasiparticles having the complex self-energy in terms of effective Hamiltonian, NH physics naturally shows up because of the life time effects from self-energy. The most important point is the emergence of gapless defective points (DPs), which lead to an open Fermi surface, such as Fermi arcs in the bulk energy spectrum.
In previous studies, it is pointed out that the effect of symmetry leads to the symmetry protected NH band touching, such as the symmetry-protected exceptional torus (SPETs). A typical example is a parity-time reversal (PT) symmetric nodal-line semimetal (NLSM).
In this study, we demonstrate how the SPETs can emerge in strongly correlated systems. We analyze correlated NLSM on a diamond lattice model with a sublattice dependent on-site Hubbard interaction by using the dynamical mean-field theory. First, we reveal the emergence of a SPET unique to NH physics with many-body chiral symmetry, which forms the 3D open Fermi surface locked on the Fermi level. We further elucidate that the static susceptibility for a sublattice with weak interaction is enhanced by the emergence of SPETs.   

Realizing the Majorana Quasiparticle fermionic dynamics in \emph{(1+1)} dimensional Topological Quantum Materials

A Majorana fermion and its dynamics are determined by the Majorana equation having equal values of spinor and conjugate field, thereby making topological quantum material a technological reality [\emph{Phys. Rev. Lett.} $\bf{121}$, 067701, 2018]. It is interesting to study the dynamics of Majorana fermions in presence of external perturbations in \emph{(1+1)} dimensions, a scalar potential by approaching for the first time implementing the methods of supersymmetric quantum mechanics [\emph{Phys. Rev. Lett.} $\bf{106}$, 060503, 2011; \emph{Rev. Mod. Phys.} $\bf{80}$, 1083, 2008]. Moreover, the dynamics of two competing effects (i.e. strain and magnetic field) is worth to focus in monolayer quantum material with the aim to explore its impact in various phenomena of quantum field theory, such as induced charge density, magnetic catalysis, symmetry breaking, dynamical mass generation, and magnetization. The combined effect of real and pseudomagnetic fields produces an induced valley polarization creating new platforms to design quantum computers and valleytronics devices.   

Crystal-to-Fracton Tensor Gauge Theory Dualities

We discuss the duality between elasticity of two-dimensional crystals and fracton tensor gauge
theories, developed by two of the authors [1,2,3]. This duality leads to numerous predictions for the
phases and phase transitions in fracton systems, such as the existence of gauge theory counterparts
to the (commensurate) crystal, supersolid, hexatic, and isotropic fluid phases of elasticity theory,
that will be discussed. The classical finite temperature limit, provides a complementary description
of the KTHNY theory of 2D melting, formulated in terms of a higher derivative vector sine-Gordon
model. Broader implications of this duality, such as the quantum melting transitions and quantum
phase diagrams, symmetry enriched fracton order, and connection to the interacting topological
crystalline insulators, will be discussed.

[1] Michael Pretko, Zhengzheng Zhai and Leo Radzihovsky, arXiv:1907.12577 [cond-mat.str-el].
[2] M. Prekto and L. Radzihovsky, Phys. Rev. Lett. 120, 195301 (2018).
[3] M. Pretko and L. Radzihovsky, Phys. Rev. Lett. 121, 235301 (2018).   

Interactions in nodal-line semimetals with quadratic band touching

We address the problem of Coloumb interactions in 3D nodal-line semimetals with quadratic band touching using perturbative Wilsonian renormalization group approach. At one loop order, we find that the non-interacting fixed point is unstable and flows to an interacting fixed point. We compute corrections to the dynamical exponent, the screening charge and find corrections to other experimentally measurable quantities such as the specific heat, compressibility, etc. We also consider the emergence of other competing instabilities in the charge sector from short-range interactions.   

Statistical localization: from strong fragmentation to strong edge modes

Certain disorder-free Hamiltonians can be non-ergodic due to a strong fragmentation of the Hilbert space into disconnected sectors. We show how to characterize such systems by introducing the notion of 'statistically localized integrals of motion’ (SLIOM), whose eigenvalues label the connected components of the Hilbert space. SLIOMs are not spatially localized in the operator sense, but appear localized to sub-extensive regions when their expectation value is taken in typical states with a finite density of particles. We will illustrate this general concept on several Hamiltonians, both with and without dipole conservation. For the former we uncover additional SLIOMs due to dipole moment conservation on finite regions of the chain. Moreover, we explain that there exist perturbations which destroy these integrals of motion in the bulk of the system, while keeping them on the boundary. This results in statistically localized strong zero modes, leading to infinitely long-lived edge magnetizations along with a thermalizing bulk. We also show that these edge modes can lead to the appearance of topological string order in a certain subset of highly excited eigenstates, and conclude providing experimental realizations of these models using existing experimental platforms.   

Classification of topological phases in one dimensional non-hermitian systems

Topological phases in non-Hermitian systems became a fascnating subject recently. In this paper, we attempt to classify topological phases in 1D non-Hermitian systems. We begin with the non-Hermitian generalization of Su-Schrieffer-Heeger(SSH) model and discuss its many body topological Berry phase, which is well defined for any quasi hermitian systems(non-Hermitian systems that have real energy spectrum).
We then demonstrate that the classifications of topological phases for quasi hermitian systems are exactly the same as their hermitian counterparts. Moreover, we find that unitarity actually can emerge for fixed point partition function describing topological phases in 1D non-Hermitian systems with local interactions. Thus we conjecture that for 1D non-Hermitian system, the classification of topological phases are exactly the same as Hermitian systems.