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Register a new userTopological Gaps in Quasi-Periodic Spin Chains: A Numerical and K-Theoretic Analysis
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Topological phases supported by quasi-periodic spin-chain models and their bulk-boundary principles are investigated by numerical and K-theoretic methods. We show that, for both the un-correlated and correlated phases, the operator algebras that generate the Hamiltonians are non-commutative tori, hence the quasi-periodic chains display physics akin to the quantum Hall effect in two and higher dimensions. The robust topological edge modes are found to be strongly shaped by the interaction and, generically, they have hybrid edge-localized and chain-delocalized structures. Our findings lay the foundations for topological spin pumping using the phason of a quasi-periodic pattern as an adiabatic parameter, where selectively chosen quantized bits of magnetization can be transferred from one edge of the chain to the other.
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Quasi-periodic quantum spin chains were recently found to support many topological phases in the finite magnetization sectors. They can simulate strong topological phases from class A in arbitrary dimension that are characterized by first and higher order Chern numbers. In the present work, we use those findings to generate topological phases at finite magnetization densities that carry first Chern numbers. Given the reduced dimensionality of the spin chains, this provides a unique opportunity to investigate the bulk-boundary correspondence as well as the stability and quantization of the Chern number in the presence of interactions. The later is reformulated using a torus action on the algebra of observables and its quantization and stability is confirmed by numerical simulations. The relations between Chern values and the observed edge spectrum are also discussed.
We establish a direct connection between inhomogeneous XX spin chains (or free fermion systems with nearest-neighbors hopping) and certain QES models on the line giving rise to a family of weakly orthogonal polynomials. We classify all such models and their associated XX chains, which include two families related to the Lame (finite gap) quantum potential on the line. For one of these chains, we numerically compute the Renyi bipartite entanglement entropy at half filling and derive an asymptotic approximation thereof by studying the models continuous limit, which turns out to describe a massless Dirac fermion on a suitably curved background. We show that the leading behavior of the entropy is that of a $c=1$ critical system, although there is a subleading $log(log N)$ correction (where $N$ is the number of sites) unusual in this type of models.
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We report the synthesis and systematic studies of a new layered ternary telluride TaPdTe5 with quasi-one-dimensional PdTe2 chains. This compound crystalizes in a layered orthorhombic structure with space group Cmcm. Analysis of its curved field-dependent Hall resistivity, using the two-band model, indicates the hole-dominated transport with a high mobility ${mu}_h$ = 2.38 $times$ 10$^3$ cm$^2$ V$^{-1}$ s$^{-1}$ at low temperatures. The in-plane magnetoresistance (MR) displays significant anisotropy with field applied along the crystallographic $b$ axis. The MR with the current applied along the $c$-axis is also measured in high magnetic fields up to 51.7 T. Remarkably, it follows a power-law dependence and reaches (9.5 $times$ 10$^3$)% at 2.1 K without any signature of saturation. The De Haas-van Alphen oscillations show a small Fermi-surface pocket with a nontrivial Berry phase. The Shubnikov-de Haas (SdH) oscillations are detected at low temperatures and under magnetic fields above 28.5 T. Two effective masses $m^*$ (0.26$m_e$ and 0.41$m_e$) are extracted from the oscillatory SdH data. Our first-principles calculations unveil a topological Dirac cone in its surface states, and, in particular, the topological index indicates that TaPdTe$_5$ is a topologically nontrivial material.
We construct an example of a 1$d$ quasiperiodically driven spin chain whose edge states can coherently store quantum information, protected by a combination of localization, dynamics, and topology. Unlike analogous behavior in static and periodically driven (Floquet) spin chains, this model does not rely upon microscopic symmetry protection: Instead, the edge states are protected purely by emergent dynamical symmetries. We explore the dynamical signatures of this Emergent Dynamical Symmetry-Protected Topological (EDSPT) order through exact numerics, time evolving block decimation, and analytic high-frequency expansion, finding evidence that the EDSPT is a stable dynamical phase protected by bulk many-body localization up to (at least) stretched-exponentially long time scales, and possibly beyond. We argue that EDSPTs are special to the quasiperiodically driven setting, and cannot arise in Floquet systems. Moreover, we find evidence of a new type of boundary criticality, in which the edge spin dynamics transition from quasiperiodic to chaotic, leading to bulk thermalization.
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