arXiv subjects

Nicholas Sedlmayr

Publications and source records attributed to Nicholas Sedlmayr.

At least 19 recordsLinked to original sources

arXiv2026

The Two Dimensional Dynamical Bulk Boundary Correspondence: Beyond Two Band Models

A dynamical equivalent of the bulk-boundary correspondence has been suggested to occur in one and two dimensional topological models following sudden quenches. Depending on the topological invariant of the time evolving and initial phases involved large boundary contributions to a dynamical free energy occur. Moreover they occur periodically between the critical times at which this dynamical free energy becomes non-analytic, \emph{i.e.}~at dynamical quantum phase transitions. At these critical times the eigenvalue spectrum of the Loschmidt matrix which underlies the dynamical free energy closes its gap. The boundary contributions are understood to be due to zero-modes or in-gap bands of this matrix, forming a close analogy with equilibrium topological models and their edge modes. The exact cause of this phenomena and its generality remain unknown. In this article we test the dynamical bulk-boundary correspondence for a complicated two dimensional topological superconductor with a rich phase diagram, allowing quenches between many different Chern numbers. We show that there is no straightforward correspondence between the equilibrium phases quenched between and the dynamical bulk boundary correspondence. Furthermore the correspondence can depend on the orientation of the edges, suggesting a possible weak topological variant.

cond-mat.stat-mech↗

arXiv2026

On the Relation Between String Order Parameters, Entanglement, and Dynamical Quantum Phase Transitions in Topological Dynamics

Topological order is defined by topological invariants, rather than symmetries and local order parameters. Nonetheless some topological phases can be characterized by string order parameters and entanglement. In this article we study how string order parameters and entanglement spectra behave out-of-equilibrium following quenches in one dimensional topological models with $\mathbb{Z}$ invariants. Previously it has been suggested that string order parameters could serve as an experimental probe of dynamical quantum phase transitions. Despite the existence of clear zeroes in the order parameters at critical times, we show that in general there is no exact quantitative or qualitative connection with the critical times of dynamical quantum phase transitions. Another possible connection is of dynamical string order parameter zeroes and dynamical crossings at the center of entanglement spectra. Here we see that there can sometimes be a connection, but it is not typical. Again there is no general quantitative or qualitative connection. Each dynamical form of criticality behaves independently, though we do see that critical times tend to be of the same order of magnitude and give an argument for why this is the case. We also find that a string order parameter which labels one topological phase can undergo non-trivial dynamics even following a quench between \emph{other} topological phases. We elucidate where connections can be made, and where they result from a consideration of insufficiently general models. These results cast doubt on the idea of genuine dynamical phases following quenches in such models.

cond-mat.str-el↗

arXiv2026

Torsion Induced Asymmetric Luttinger Liquids

We consider a general model of a Luttinger liquid with broken parity and time reversal symmetry, but with their composite symmetry intact. Such a scenario can be due to a combination of torsion and a Zeeman field in nanowires, or a result of bringing different helical Luttinger liquids into proximity. The broken symmetries result in a band structure with no axis of symmetry, and therefore with asymmetric velocities between left and right moving contributions. By taking a general spin-full model with all possible scattering and interaction terms in the bosonic model we show that generically the spin degree of freedom becomes gapped out, resulting in an effective spinless Luttinger liquid with asymmetric velocities. Our work generalizes and extends previous studies which focused on a minimal model of a spinless Luttinger liquid. We further demonstrate that a possible experimental signature of the asymmetry of such asymmetric models can be seen in the spectral function.

cond-mat.str-el↗

arXiv2025

Dynamical Scarring from Scrambling in Two Dimensional Topological Materials

Out-of-time ordered correlators are a probe of how the information of an initial perturbation is effectively scrambled under unitary time evolution, widely used to study quantum chaos. They have also been used to demonstrate that information is trapped in the zero dimensional edge modes of topological insulators and superconductors, and does not become scrambled. Here we study scrambling in two dimensional topological models. In the bulk the butterfly velocity, the speed at which the out-of-time ordered correlator spreads, gains a directional dependence from the underlying lattice. Furthermore when there are chiral or helical edge modes present these cause a form of dynamical scarring. The information about an initial perturbation on the boundary of the system travels around the edge, carried by the edge modes, but is not scrambled over very long time scales. The direction and speed of the scars are given by the velocities of the linearly dispersing edge modes. We further show that these scars do not interact, passing through each other. We back up these results with analytical and numerical calculations on exemplary models.

cond-mat.stat-mech↗

arXiv2025

A Dynamical Bulk-Boundary Correspondence in Two Dimensional Topological Matter

We provide strong numerical evidence for a dynamical bulk-boundary correspondence in two-dimensional topological matter which manifests itself as boundary contributions to the dynamical free energy and is governed by a two-dimensional non-Hermitian dynamical Loschmidt matrix -- a setting largely unexplored beyond one dimension. Following a quantum quench, in-gap bands emerge in the spectrum of the Loschmidt matrix between successive dynamical quantum phase transitions when the time-evolving Hamiltonian is topological, while they are absent for quenches into the trivial phase in all cases we have studied. By fitting these in-gap bands, we show that they account for the observed boundary contributions to the dynamical free energy thus supporting a direct connection between the spectrum of a non-Hermitian dynamical matrix and topological boundary contributions. Taken together with earlier studies of the one-dimensional case, our results provide a framework to understand and classify dynamical topological phenomena based on the spectral properties of certain non-Hermitian matrices.

cond-mat.stat-mech↗

arXiv2024

Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models

Dynamical quantum phase transitions are non-analyticities in a dynamical free energy (or return rate) which occur at critical times. Although extensively studied in one dimension, the exact nature of the non-analyticity in two and three dimensions has not yet been fully investigated. In two dimensions, results so far are known only for relatively simple two-band models. Here we study the general two- and three-dimensional cases. We establish the relation between the non-analyticities in different dimensions, and the functional form of the densities of Fisher zeroes. We show, in particular, that entering a critical region where the density of Fisher zeroes is non-zero at the boundary always leads to a cusp in the derivative of the return rate while the return rate itself is smooth. We illustrate our results by obtaining analytical results for exemplary two- and three-dimensional models.

cond-mat.stat-mech↗

arXiv2024

Information propagation in one-dimensional XY-$Γ$ chains

The bond-dependent Kitaev model offers a playground in which one can search for quantum spin liquids. In these Kitaev materials, a symmetric off-diagonal $Γ$ term emerges, hosting a number of remarkable features, which has been particularly challenging to fully understand. One primary question that arises after recognizing a new phase is how information will spread in it. Out-of-time-ordered commutators and entanglement entropy describe processes whereby information about the initial condition of a unitarily evolving system propagates over the system. A possible way to investigate dynamics in such systems is by considering one-dimensional models. We investigate here the one-dimensional spin-1/2 XY model in a transverse field with a $Γ$ interaction with periodic boundary conditions imposed. We will show that the $Γ$ interaction constructs an asymmetric "light-cone" with different butterfly velocities. In addition, it leads to faster information propagation in the spiral phase and slower propagation in the ferromagnetic and paramagnetic phases. Interestingly, we observe a pronounced effect in the entanglement entropy, explicitly showing up as a two-stage linear growth in time as fast/slow then slow/fast for quenches originating from the spiral phase. We hope our work paves the way for studying more about the spreading of information in one-dimensional Kitaev materials, which can in turn help to discover unknown aspects of higher-dimensional models.

cond-mat.str-el↗

arXiv2024

The dynamical bulk boundary correspondence and dynamical quantum phase transitions in the Benalcazar-Bernevig-Hughes model

In this article we demonstrate that dynamical quantum phase transitions occur for an exemplary higher order topological insulator, the Benalcazar-Bernevig-Hughes model, following quenches across a topological phase boundary. A dynamical bulk boundary correspondence is also seen both in the eigenvalues of the Loschmidt overlap matrix and the boundary return rate. The latter is found from a finite size scaling analysis for which the relative simplicity of the model is crucial. Contrary to the usual two dimensional case the dynamical quantum phase transitions in this model show up as cusps in the return rate, as for a one dimensional model, rather than as cusps in its derivative as would be typical for a two dimensional model. We explain the origin of this behaviour.

cond-mat.mes-hall↗

arXiv2023

Information Trapping by Topologically Protected Edge States: Scrambling and the Butterfly Velocity

Topological insulators and superconductors have attracted considerable attention, and many different theoretical tools have been used to gain insight into their properties. Here we investigate how perturbations can spread through exemplary one-dimensional topological insulators and superconductors using out-of-time ordered correlators. Out-of-time ordered correlators are often used to consider how information becomes scrambled during quantum dynamics. The wavefront of the out-of-time ordered correlator can be ballistic regardless of the underlying system dynamics, and here we confirm that for topological free fermion systems the wavefront spreads linearly at a characteristic butterfly velocity. We pay special attention to the topologically protected edge states, finding that "information" can become trapped in the edge states and essentially decoupled from the bulk, surviving for relatively long times. We consider different models with multiple possible edge states coexisting on a single edge.

cond-mat.mes-hall↗

arXiv2023

Quantized Thermal Hall Conductance and the Topological Phase Diagram of a Superconducting Bismuth Bilayer

Two dimensional topological superconductors with chiral edge modes are predicted to posses a quantized thermal Hall effect proportional to the Chern number, exactly half that for chiral topological insulators. However not much work has been done in identifying the quantized heat conductance in the literature, even for some of the standard models of topological superconductivity. Here we introduce a model based on a proximity induced superconducting Bismuth bilayer, and directly calculate the thermal Hall conductance of this lattice model. This model serves as a demonstration of the state of the art possible in such a calculation, as well as introducing an interesting paradigmatic topological superconductor with a rich phase diagram. We demonstrate the quantized thermal Hall plateaus in several different topological phases, and compare this to numerical calculations of the Chern number, as well as analytical calculations of the Chern number's parity invariant. We demonstrate that it is possible to get a reasonable topological phase diagram from the quantized thermal Hall calculations. The technique used can be applied to wide range of models directly in real space.

cond-mat.mes-hall↗

arXiv2023

Dynamical Quantum Phase Transitions Following Double Quenches: Persistence of the Initial State vs Dynamical Phases

Dynamical quantum phase transitions can occur following quenches in quantum systems when the rate function, a dynamical analogue of the free energy, becomes non-analytic at critical times. Here we exhaustively investigate in an exemplary model how the dynamically evolving state responds to a second quench. We demonstrate that for quenches where the initial and final Hamiltonian belong to different phases always result in dynamical quantum phase transitions, irrespective of the intermediate quench and dynamics or the time of the second quench. However, if the initial and final Hamiltonian belong to the same equilibrium phase then the intermediate Hamiltonian must belong to a different phase. In this case, the second quench time in relation to the critical times of the first quench becomes crucial to the existence of dynamical quantum phase transitions.

cond-mat.stat-mech↗

arXiv2023

Hinge States of Second-Order Topological Insulators as a Mach-Zehnder Interferometer

Three-dimensional higher-order topological insulators can have topologically protected chiral modes propagating on their hinges. Hinges with two co-propagating chiral modes can serve as a "beam splitter" between hinges with only a single chiral mode. Here we show how such a crystal, with Ohmic contacts attached to its hinges, can be used to realize a Mach-Zehnder interferometer. We present concrete calculations for a lattice model of a first-order topological insulator in a magnetic field, which, for a suitable choice of parameters, is an extrinsic second-order topological insulator with the required configuration of chiral hinge modes.

cond-mat.mes-hall↗

arXiv2022

Superconductivity in monolayer and few-layer graphene: III Impurity-induced subgap states and quasi-particle interference patterns

We consider the most energetically favorable symmetry-allowed spin-singlet and spin-triplet superconducting pairing symmetries in monolayer and few-layer graphene, and for each calculate the energy spectrum in the presence of a scalar or magnetic impurity. We find that two doubly degenerate subgap states exist for scalar impurities for all types of pairing, except for the spin-singlet $s$-wave state. For magnetic impurities, two or four subgap states may form depending on the order parameter symmetry. We find that the spin polarization of these states allows one to distinguish between spin-singlet and triplet pairing, for example, only the spin-triplet states show opposite-energy subgap states with the same spin. We also calculate the quasi-particle interference patterns associated with the subgap states and find that they exhibit features that could distinguish between different types of pairing symmetries, especially a breaking of rotational symmetry for nodal states, stronger for the spin-singlet $d_{xy}$ and $d_{x^2-y^2}$ than for the spin-triplet $p_x$ and $p_y$ states.

cond-mat.supr-con↗

arXiv2022

Superconductivity in monolayer and few-layer graphene: II. Topological edge states and Chern numbers

We study the emergence of electronic edge states in superconducting (SC) monolayer, bilayer, and trilayer graphene for both spin-singlet and spin-triplet SC order parameters. We focus mostly on the gapped chiral $p+ip'$- and $d+id'$-wave SC states that show a non-zero Chern number and a corresponding number of edge states. For the $p+ip'$-wave state, we observe a rich Chern phase diagram when tuning the chemical potential and the SC order parameter amplitudes, which depends strongly on the number of layers and their stacking, and is also modified by trigonal warping. At small parameter values we observe a region whose Chern number is unique to rhombohedrally stacked graphene, and is independent of the number of layers. Our results can be understood in relation not only to the SC order parameter winding as expected, but also to the normal state band structure. This observation establishes the importance of the normal state characteristics for understanding the topology in SC graphene systems.

cond-mat.supr-con↗

arXiv2021

Dynamical quantum phase transitions in a mesoscopic superconducting system

We inspect signatures of dynamical quantum phase transitions driven by two types of quenches acting on a correlated quantum dot embedded between superconducting and metallic reservoirs. Under stationary conditions the proximity induced on-dot pairing combined with the strong Coulomb repulsion prefers the quantum dot to be either in the singly occupied (spinful) or BCS-type (spinless) ground state configuration. We study the time evolution upon traversing such a phase boundary due to quantum quenches by means of the time-dependent numerical renormalization group approach, revealing non-analytic features in the low-energy return rate. Quench protocols can be realized in a controllable manner and we are confident that detection of this dynamical singlet-doublet phase transition would be feasible by the charge tunnelling spectroscopy.

cond-mat.mes-hall↗

arXiv2021

Instability of Majorana states in Shiba chains due to leakage into a topological substrate

We revisit the problem of Majorana states in chains of scalar impurities deposited on a superconductor with a mixed s-wave and p-wave pairing. We also study the formation of Majorana states for magnetic impurity chains. We find that the magnetic impurity chains exhibit well-localized Majorana states when the substrate is trivial, but these states hybridize and get dissolved in the bulk when the substrate is topological. Most surprisingly, and contrary to previous predictions, the scalar impurity chain does not support fully localized Majorana states except for very small and finely tuned parameter regimes, mostly for a non-topological substrate close to the topological transition. Our results indicate that a purely p-wave or a dominant p-wave substrate are not good candidates to support either magnetic or scalar impurity topological Shiba chains.

cond-mat.supr-con↗

arXiv2021

Analytical and semianalytical tools to determine the topological character of Shiba chains

We introduce three new analytical and semi-analytical tools that allow one to determine the topological character of impurity Shiba chains. The analytical methods are based on calculating the effective Green's function of an infinite embedded chain using the T-matrix formalism and describing the chain as a {\it line impurity}. We thus provide a solution to the longstanding size-effects problem affecting the only general alternative method, the numerical tight-binding analysis. As an example we consider a chain of magnetic impurities deposited on an s-wave superconducting substrate with Rashba spin-orbit and we calculate its topological phase diagram as a function of the magnetic impurity strength and the chemical potential. We find a perfect agreement between all our new techniques and a numerical analysis.

cond-mat.supr-con↗

arXiv2021

Unconventional topological transitions in a self-organized magnetic ladder

It is commonly assumed that topological phase transitions in topological superconductors are accompanied by a closing of the topological gap or a change of the symmetry of the system. We demonstrate that an unconventional topological phase transition with neither gap closing nor a change of symmetry is possible. We consider a nanoscopic length ladder of atoms on a superconducting substrate, comprising self-organized magnetic moments coupled to itinerant electrons. For a range of conditions, the ground state of such a system prefers helical magnetic textures, self-sustaining topologically nontrivial phase. Abrupt changes in the magnetic order as a function of induced superconducting pairing or chemical potential can cause topological phase transitions without closing the topological gap. Furthermore, the ground state prefers either parallel or anti-parallel configurations along the rungs, and the anti-parallel configuration causes an emergent time reversal asymmetry protecting Kramer's pair's of Majorana zero modes, but in a BDI topological superconductor. We determine the topological invariant and inspect the boundary Majorana zero modes.

cond-mat.supr-con↗