Strongly interacting topological states in multi-particle quantum systems pose great challenges to both theory and experiment. Recently, bound states of elementary spin waves (magnons) in quantum magnets have been experimentally observed in quantum Heisenberg chains comprising ultracold Bose atoms in optical lattices. Here, we explore a strongly interacting topological state called topological magnon bound-state in the quantum Heisenberg chain under cotranslational symmetry. We find that the cotranslational symmetry is the key to the definition of a topological invariant for multi-particle quantum states, which enables us to characterize the topological features of multi-magnon excitations. We calculate energy spectra, density distributions, correlations and Chern numbers of the two-magnon bound-states and show the existence of topological protected edge bound-states. Our study not only opens a new prospect to pursue topological magnon bound-states, but also gives insights into the characterization and understanding of strongly interacting topological states.
The studies of multi-magnon excitations will extend our understandings of quantum magnetism and strongly correlated matters. Here, by using the time-evolving block decimation algorithm, we investigate the Bloch oscillations of two-magnon excitations under a gradient magnetic field. Through analyzing the symmetry of the Hamiltonian, we derive a rigorous and universal relation between ferromagnetic and anti-ferromagnetic systems. Under strong interactions, in addition to free-magnon Bloch oscillations, there appear fractional bounded-magnon Bloch oscillations which can be understood by an effect…
We apply continuous similarity transformations (CSTs) to the easy-axis antiferromagnetic XXZ-model on the square lattice. The CST flow equations are truncated in momentum space by the scaling dimension $d$ so that all contributions with $d\le 2$ are taken into account. The resulting quartic magnon-conserving effective Hamiltonian is analyzed in the zero-, one-, and two-magnon sector. In this way, a quantitative description of the ground-state energy, the one-magnon dispersion and its gap as well as of two-magnon bound states is gained for anisotropies ranging from the gapped Ising model to the…
We solve few-magnon problems for a finite-size spin-$S$ periodic Heisenberg XXZ chain with single-ion anisotropy through constructing sets of exact Bloch states achieving block diagonalization of the system. Concretely, the two-magnon (three-magnon) problem is converted to a single-particle one on a one-dimensional (two-dimensional) effective lattice whose size depends linearly (quadratically) on the total number of sites. For parameters lying within certain ranges, various types of multimagnon bound states are manifested and shown to correspond to edge states on the effective lattices. In the…
The XXZ model on a square lattice in the presence of a transverse magnetic field is studied within the spin wave theory to investigate the resulting canted antiferromagnet. The small and large field regimes are probed separately both for easy-axis and easy-plane scenarios which reveal an unentangled factorized ground state at an intermediate value of the field. Goldstone modes are obtained for the field-free $XY$ antiferromagnet as well as for the isotropic antiferromagnet with field up to its saturation value. Moreover, for an easy-plane anisotropy, we find that there exists a non-zero field,…
We compute the spin structure factor of XXZ spin chains in the Heisenberg and gapped (Ising) regimes in the high-temperature limit for nonzero magnetization, within the framework of generalized hydrodynamics including diffusive corrections. The structure factor shows a hierarchy of timescales in the gapped phase, owing to $s$-spin magnon bound states (`strings') of various sizes. Although short strings move ballistically, long strings move primarily diffusively as a result of their collisions with short strings. The interplay between these effects gives rise to anomalous power-law decay of the…
It is still an outstanding challenge to characterize and understand the topological features of strongly interacting states such as bound-states in interacting quantum systems. Here, by introducing a cotranslational symmetry in an interacting multi-particle quantum system, we systematically develop a method to define a Chern invariant, which is a generalization of the well-known Thouless-Kohmoto-Nightingale-den Nijs invariant, for identifying strongly interacting topological states. As an example, we study the topological multi-magnon states in a generalized Heisenberg XXZ model, which can be …
Since longitudinal spin-spin interaction is ubiquitous in magnetic materials, it is very interesting to explore the interplay between topology and longitudinal spin-spin interaction. Here, we examine the role of longitudinal spin-spin interaction on topological magnon excitations. Remarkably, even for single-magnon excitations, we discover topological edge states and defect edge states of magnon excitations in a dimerized Heisenberg XXZ chain and their topological properties can be distinguished via adiabatic quantum transport. We uncover topological phase transitions induced by longitudinal s…
We show that the dynamics of a doubly-excited 1D Heisenberg ferromagnetic chain, subject to short pulses from a parabolic magnetic field may be analyzed as a pair of quantum kicked rotors. By focusing on the two-magnon dynamics in the kicked XXZ model we investigate how the anisotropy parameter - which controls the strength of the magnon-magnon interaction - changes the nature of the coupling between the two "image" coupled Kicked Rotors. We investigate quantum state transfer possibilities and show that one may control whether the spin excitations are transmitted together, or separate from eac…
We calculate exactly the entanglement content of magnon excited states in the integrable spin-1/2 XXX and XXZ chains in the scaling limit. In particular, we show that as far as the number of excited magnons with respect to the size of the system is small one can decompose the entanglement content, in the scaling limit, to the sum of the entanglement of particular excited states of free fermionic or bosonic theories. In addition we conjecture that the entanglement content of the generic translational invariant free fermionic and bosonic Hamiltonians can be also classified, in the scaling limit,…
The nonlinear effect of a driving force in periodically driven quantum many-body systems can be systematically investigated by analyzing the effective Floquet Hamiltonian. In particular, under an appropriate definition of the effective Hamiltonian, simple driving forces may result in non-local interactions. Here we consider a driven $ XXZ $ model to show that four-site interactions emerge owing to the driving force, which can produce state-selective localization, a phenomenon where some limited Ising-like product states become fixed points of dynamics. We first derive the effective Hamiltonian…
Emergent prethermal Bethe integrability in a periodically driven Rydberg chain
School of Physical Sciences, Indian Association for the Cultivation of Science（印度科学文化促进协会物理科学学院）；Center for High Energy Physics, Indian Institute of Science（印度科学院高能物理中心）
Quantum information storage using charge-neutral quasiparticles are expected to play a crucial role in the future of quantum computers. In this regard, magnons or collective spin-wave excitations in solid-state materials are promising candidates in the future of quantum computing. Here, we study the quantum squeezing of Dirac and topological magnons in a bosonic honeycomb optical lattice with spin-orbit interaction by utilizing the mapping to quantum spin-$1/2$ XYZ Heisenberg model on the honeycomb lattice with discrete Z$_2$ symmetry and a Dzyaloshinskii-Moriya interaction. We show that the s…
We analyze the properties of low-energy bound states in the transverse-field Ising model and in the XXZ model on the square lattice. To this end, we develop an optimized implementation of perturbative continuous unitary transformations. The Ising model is studied in the small-field limit which is found to be a special case of the toric code model in a magnetic field. To analyze the XXZ model, we perform a perturbative expansion about the Ising limit in order to discuss the fate of the elementary magnon excitations when approaching the Heisenberg point.
Ultracold two-level atoms in optical lattices offer an excellent experimental platform to explore magnon excitations [Fukuhara et al 2013 Nat. Phys. 9, 235; Fukuhara et al 2013 Nature 502, 76]. Here, we investigate how gradient magnetic field and periodically modulated tunneling strength affect the two-magnon excitations in these ultracold atomic systems. In the resonant condition where the driving frequency matches and smooths the potential bias, the system gains translational invariance in both space and time in the rotating frame, and thus we can develop a Floquet-Bloch band theory for two …
We investigate the effect of periodic driving by an external field on systems with attractive pairing interactions. These include spin systems (like the ferromagnetic XXZ model) as well as ultracold fermionic atoms described by the attractive Hubbard model. We show that a well-known phenomenon seen in periodically driven systems--the renormalization of the exchange coupling strength--acts selectively on bound-pairs of spins/atoms, relative to magnon/bare atom states. Thus one can control the direction and speed of transport of bound-pair relative to magnon/unpaired atom states, and thus cohere…
We study the rectification of spin current in $XXZ$ chains segmented in two parts, each with a different anisotropy parameter. Using exact diagonalization and a matrix product states algorithm we find that a large rectification (of the order of $10^4$) is attainable even using a short chain of $N=8$ spins, when one half of the chain is gapless while the other has large enough anisotropy. We present evidence of diffusive transport when the current is driven in one direction and of a transition to an insulating behavior of the system when driven in the opposite direction, leading to a perfect di…
We explore the edge defects induced by spin-spin interaction in a finite paradigmatic Heisenberg spin chain. By introducing a gradient magnetic field and a periodically-modulated spin-exchange strength, the resonance between modulation frequency and magnetic field gradient can also induce asymmetric defects at the edges, dubbed as Floquet-Wannier-Zeeman edge defects. The interplay between these two types of edge defects allows us to manipulate the magnon edge states from an isolated band into a continuum one. In the high-frequency regime, we analytically derive effective models to interpret th…
A minimal model of a quantum refrigerator (QR), i.e. a periodically phase-flipped two-level system permanently coupled to a finite-capacity bath (cold bath) and an infinite heat dump (hot bath), is introduced and used to investigate the cooling of the cold bath towards the absolute zero (T=0). Remarkably, the temperature scaling of the cold-bath cooling rate reveals that it does not vanish as T->0 for certain realistic quantized baths, e.g. phonons in strongly disordered media (fractons) or quantized spin-waves in ferromagnets (magnons). This result challenges Nernst's third-law formulation kn…
Periodic orbits and quantum many-body scars in integrable spin chains
Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）；Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
In this review the debated rapport between thermodynamics and quantum mechanics is addressed in the framework of the theory of periodically-driven/controlled quantum-thermodynamic machines. The basic model studied here is that of a two-level system (TLS), whose energy is periodically modulated while the system is coupled to thermal baths. When the modulation interval is short compared to the bath memory time, the system-bath correlations are affected, thereby causing cooling or heating of the TLS, depending on the interval. In steady state, a periodically-modulated TLS coupled to two distinct …
We study quantum chaos and spectral correlations in periodically driven (Floquet) fermionic chains with long-range two-particle interactions, in the presence and absence of particle number conservation ($U(1)$) symmetry. We analytically show that the spectral form factor precisely follows the prediction of random matrix theory in the regime of long chains, and for timescales that exceed the so-called Thouless/Ehrenfest time which scales with the size $L$ as ${\cal O}(L^2)$, or ${\cal O}(L^0)$, in the presence, or absence of $U(1)$ symmetry, respectively. Using random phase assumption which ess…
A method of switching a controlled-NOT gate in a solid-stae NMR quantum computer is presented. Qubits of I=1/2 nuclear spins are placed periodically along a quantum spin chain (1-D antiferromagnet) having a singlet ground state with a finite spin gap to the lowest excited state caused by some quantum effect. Irradiation of a microwave tuned to the spin gap energy excites a packet of triplet magnons at a specific part of the chain where control and target qubits are involved. The packet switches on the Suhl-Nakamura interaction between the qubits, which serves as a controlled NOT gate. The qubi…
