The bulk-boundary correspondence relates quantized edge states to bulk topological invariants in topological phases of matter. In one-dimensional symmetry-protected topological systems (SPTs), quantized topological Thouless pumps directly reveal this principle and provide a sound mathematical foundation. Symmetry-protected higher-order topological phases of matter (HOSPTs) also feature a bulk-boundary correspondence, but its connection to quantized charge transport remains elusive. Here we show that quantized Thouless pumps connecting $C_4$-symmetric HOSPTs can be described by a tuple of four Chern numbers that measure quantized bulk charge transport in a direction-dependent fashion. Moreover, this tuple of Chern numbers allows to predict the sign and value of fractional corner charges in the HOSPTs. We show that the topologically non-trivial phase can be characterized by both quadrupole and dipole configurations, shedding new light on current debates about the multi-pole nature of the HOSPT bulk. By employing corner-periodic boundary conditions, we generalize Restas's theory to HOSPTs. Our approach provides a simple framework for understanding topological invariants of general HOSPTs and paves the way for an in-depth description of future dynamical experiments.
We elucidate the mechanism for instability of topological Thouless pumping in strongly interacting systems from a viewpoint of symmetry-protected topological phases. If the protecting symmetries of the underlying topological phases change between noninteracting fermions and a bosonic system in the strong coupling limit, the symmetry protection argument enforces a gap closing and thereby predicts a breakdown of the topological pumping. We also demonstrate that, even in the weakly interacting regime where the bulk topological pumping is still robust, the interaction effects manifest themselves i…
The Thouless pump is a phenomenon in which $\mathrm{U}(1)$ charges are pumped from an edge of a fermionic system to another edge. The Thouless pump has been generalized in various dimensions and for various charges. In this paper, we investigate the generalized Thouless pumps of fermion parity in both trivial and non-trivial phases of $1+1$-dimensional interacting fermionic short range entangled (SRE) states. For this purpose, we use matrix product states (MPSs). MPSs describe many-body systems in $1+1$ dimensions, and can characterize SRE states algebraically. We prove fundamental theorems fo…
We define and study analogs of the Thouless charge pump for many-body gapped systems in dimension $D$. We show how to attach a topological invariant to a $D$-dimensional family of such systems, provided all of them have an on-site $U(1)$ symmetry. For a large class of families we argue that this topological invariant is an integer. In the case of gapped systems of free fermions in two dimensions, the invariant can be expressed in terms of the curvature of the Bloch-Berry connection. We also obtain a new formula for the Thouless charge pump in 1d which involves only static linear response and i…
When it comes to applying the adiabatic theorem in practice, the key question to be answered is how slow "slowly enough" is. This question can be an intricate one, especially for many-body systems, where the limits of slow driving and large system size may not commute. Recently we have shown how the quantum adiabaticity in many-body systems is related to the generalized orthogonality catastrophe [Phys. Rev. Lett. 119, 200401 (2017)]. We have proven a rigorous inequality relating these two phenomena and applied it to establish conditions for the quantized transport in the topological Thouless p…
We study a Thouless pump realized with an elastically \textit{deformable quantum dot} whose center of mass follows a non-linear stochastic dynamics. The interplay of noise, non-linear effects, dissipation and interaction with an external time-dependent driving on the pumped charge is fully analyzed. The results show that the quantum pumping mechanism not only is not destroyed by the force fluctuations, but it becomes stronger when the forcing signal frequency is tuned close to the resonance of the vibrational mode. The robustness of the quantum pump with temperature is also investigated and an…
We study the nontrivial topology of the parameter space of general $U(1)$-symmetric fermionic non-degenerately gapped system and its consequences on the transport properties in arbitrary dimensions. By a nonlinear parameter-gauge topological response theory, we find that such nontrivial topology can impose quantization constraints on the charge transport in the presence of background fluxes or, more generally, instantons in general dimensions and our result generalizes the Thouless pump and its higher dimensional generalizations. We also show that these nontrivial transport properties are rela…
We construct an interacting integrable Floquet model featuring quasiparticle excitations with topologically nontrivial chiral dispersion. This model is a fully quantum generalization of an integrable classical cellular automaton. We write down and solve the Bethe equations for the generalized quantum model, and show that these take on a particularly simple form that allows for an exact solution: essentially, the quasiparticles behave like interacting hard rods. The generalized thermodynamics and hydrodynamics of this model follow directly. Although the model is interacting, its unusually simpl…
Quantum many-body edge and extended magnon excitations from the 1/3 -- plateau of the anisotropic Heisenberg model on an open AB$_2$ chain in a magnetic field $h$ are unveiled using the density matrix renormalization group and exact diagonalization. By tuning both the anisotropy and $h$ in the rich phase diagram, the edge states penetrate in the bulk, whose gap closes in a symmetry-protected topological Kosterlitz-Thouless transition. Also, we witness the squeezed chain effect, the breaking of the edge states degeneracy, and a topological change of the excitations from gapped magnons with quad…
We show that in excitonic insulators with $s$-wave electron-hole pairing, an applied electric field (either pulsed or static) can induce a $p$-wave component to the order parameter, and further drive it to rotate in the $s+ip$ plane, realizing a Thouless charge pump. In one dimension, each cycle of rotation pumps exactly two electrons across the sample. Higher dimensional systems can be viewed as a stack of one dimensional chains in momentum space in which each chain crossing the fermi surface contributes a channel of charge pumping. Physics beyond the adiabatic limit, including in particular …
We show that in a system of one dimensional spinless fermions a topological phase and phase transition can emerge only through interaction. By allowing a dimerized or bond-alternating nearest neighbour interaction we show that the system exhibits a symmetry protected topological phase while its non-interacting limit is a gapless state. The non-trivial topological character appears due to the onset of two degenerate bond-order phases as a function of dimerized interaction which are found to be topologically distinct from each other. As a result a topological phase transition occurs between thes…
Frustrated spin-$1/2$ XXZ zigzag chains relevant to Rb$_2$Cu$_2$Mo$_3$O$_{12}$ are revisited in the light of symmetry-protected topological (SPT) phases. Using a density-matrix renormalization group method for infinite systems, we identify projective representations for four distinct time-reversal invariant SPT phases; two parity-symmetric dimer phases near the Heisenberg and XX limits and two parity-broken vector-chiral (VC) dimer phases in between. A small bond alternation in the nearest-neighbor ferromagnetic exchange coupling induces a direct SPT transition between the two distinct VC dime…
We investigate charge pumping in the vicinity of order-obstructed topological phases, i.e. symmetry protected topological phases masked by spontaneous symmetry breaking in the presence of strong correlations. To explore this, we study a prototypical Su-Schrieffer-Heeger model with finite-range interaction that gives rise to orbital charge density wave order, and characterize the impact of this order on the model's topological properties. In the ordered phase, where the many-body topological invariant loses quantization, we find that not only is quantized charge pumping still possible, but it i…
It has recently been established that cluster-like states -- states that are in the same symmetry-protected topological phase as the cluster state -- provide a family of resource states that can be utilized for Measurement-Based Quantum Computation. In this work, we ask whether it is possible to prepare cluster-like states in finite time without breaking the symmetry protecting the resource state. Such a symmetry-preserving protocol would benefit from topological protection to errors in the preparation. We answer this question in the positive by providing a Hamiltonian in one higher dimension …
The notion of topological (Thouless) pumping in topological phases is traditionally associated with Laughlin's pump argument for the quantization of the Hall conductance in two-dimensional (2D) quantum Hall systems. It relies on magnetic flux variations that thread the system of interest without penetrating its bulk, in the spirit of Aharonov-Bohm effects. Here we explore a different paradigm for topological pumping induced, instead, by magnetic flux variations $δχ$ inserted through the bulk of topological phases. We show that $δχ$ generically controls the analog of a topological pump, accompa…
Based on a topological transition of the symmetry protected topological phase (SPT), an interaction induced topological charge pump (iTCP) is proposed with the symmetry breaking parameter as a synthetic dimension. It implies that the phase boundary of the SPT is the topological obstruction although iTCP and the gap closing singularity is stable for symmetry breaking perturbations. We have confirmed the bulk-edge correspondence for this iTCP using DMRG for the Rice-Mele model with nearest-neighbor interactions. As for a realization in optical lattices, an interaction sweeping pump protocol is p…
We discuss a current dynamics on the surface of a 3-dimensional topological insulator induced by magnetization precession of a ferromagnet attached. It is found that the magnetization dynamics generates a direct charge current when the precession axis is within the surface plane. This rectification effect is due to a quantum anomaly and is topologically protected. The robustness of the rectification effect against first-varying exchange field and impurities is confirmed by explicit calculation.
We propose a one-dimensional electron model with parameters modulated adiabatically in closed cycles, which can continuously pump spin to leads. By defining the spin-polarized Wannier functions, we show that the spin pump is protected by the spin Chern numbers, so that it is stable to perturbations violating the time-reversal symmetry and spin conservation. Our work demonstrates the possibility and principle to realize topological spin pumps independent of any symmetries, and also suggests a possible way to experimentally observe the bulk topological invariants.
When adiabatically varied in time, certain one-dimensional band insulators allow for the quantized noiseless pumping of spin even in the presence of strong spin orbit scattering. These spin pumps are closely related to the quantum spin Hall system, and their properties are protected by a time-reversal restriction on the pumping cycle. In this paper we study pumps formed of one-dimensional insulators with a time-reversal restriction on the pumping cycle and a bulk energy gap which arises due to interactions. We find that the correlated gapped phase can lead to novel pumping properties. In parti…
Topological Phenomena Protected by Diabolical Textures
Harish-Chandra Research Institute (HRI)（哈里什-钱德拉研究所（HRI））；University of Texas at Dallas（德克萨斯大学达拉斯分校）；National Institute of Technology (NIT), Rourkela（鲁尔克拉国家理工学院（NIT））；Homi Bhabha National Institute (HBNI)（霍米·巴巴国家研究所（HBNI））
We study aspects of Berry phase in gapped many-body quantum systems by means of effective field theory. Once the parameters are promoted to spacetime-dependent background fields, such adiabatic phases are described by Wess-Zumino-Witten (WZW) and similar terms. In the presence of symmetries, there are also quantized invariants capturing generalized Thouless pumps. Consideration of these terms provides constraints on the phase diagram of many-body systems, implying the existence of gapless points in the phase diagram which are stable for topological reasons. We describe such diabolical points, …
The topological property in one dimension (1D) is protected by symmetry. Based on a concrete model, we show that since a 1D topological model usually contain two of the three Pauli matrix, the left one automatically become the protecting symmetry. We study the effect of disorder preserving or breaking the symmetry and show the nature of symmetry protecting in the 1D topological phase. Based on the 1D topological model, a stable quantum pumping can be constructed, which is topologically nontrivial and can be characterized by the Chern number. By calculating the instantaneous local current we sh…
