Finitely correlated states on quantum spin chains

We study a construction that yields a class of translation invariant states on quantum spin chains, characterized by the property that the correlations across any bond can be modeled on a finite-dimensional vector space. These states can be considered as generalized valence bond states, and they are dense in the set of all translation invariant states. We develop a complete theory of the ergodic decomposition of such states, including the decomposition into periodic Néel ordered states. The ergodic components have exponential decay of correlations. All states considered can be obtained as local functions of states of a special kind, so-called purely generated states, which are shown to be ground states for suitably chosen finite range VBS interactions. We show that all these generalized VBS models have a spectral gap. Our theory does not require symmetry of the state with respect to a local gauge group. In particular we illustrate our results with a one-parameter family of examples which are not isotropic except for one special case. This isotropic model coincides with the one-dimensional antiferromagnet, recently studied by Affleck, Kennedy, Lieb, and Tasaki.     

一维量子子自自旋链中拓扑有序态的物理描述

一维量子多体系统是凝聚态物理学中的重要研究方向之一,其中的新奇量子物态则是重要的研究课题。本文我们首先简要回顾一维量子整数自旋链体系的相关研究背景,然后提出一类SO(n)对称的严格可解量子自旋链模型及其矩阵乘积基态。当奇数n≥3时,体系的基态为Haldane相。利用这类态中隐藏的稀薄反铁磁序,我们找到了刻画这类态的非局域弦序参量,并在隐藏拓扑对称性的统一框架下解释了稀薄反铁磁序以及边缘态等奇特现象的起源。当偶数n≥4时,体系的基态为二聚化态。这些态属于破缺平移对称性的非Haldane相,但同样具有隐藏的反铁磁序。通过这些严格解的研究,我们还得到了一维SO(n)对称的双线性–双二次模型的基态相图,并发现在n≥5时,一维SO(n)对称的反铁磁海森堡模型的基态处于二聚化相中。基于以上这些结果,我们推广构造了一维平移不变且包含李群G对称性的Valence BondState(VBS)态,并利用其矩阵乘积表示讨论了对应哈密顿量的构造方法。对于自旋为S的量子整数自旋链,我们研究了两类具有不同拓扑属性的VBS类,前一类VBS态的边缘态处于SU(2)自旋J的不可约表示,后一类VBS态的边缘态为SO(2S+1)旋量。在前一类态中,我们以自旋为1的费米型VBS态为例构造了对应的哈密顿量。对后一类态,我们证明了它们等价于SO(2S+1)矩阵乘积态,从而揭示了呈展对称性的起源和边缘态的性质。我们还推广了SO(5)对称的玻色型和费米型VBS态,并探讨了它们的拓扑刻画方式。     

Non-ergodic states induced by impurity levels in quantum spin chains

The semi-infinite XY spin chain with an impurity at the boundary has been chosen as a prototype of interacting many-body systems to test for non-ergodic behavior. The model is exactly solvable in analytic way in the thermodynamic limit, where energy eigenstates and the spectrum are obtained in closed form. In addition of a continuous band, localized states may split off from the continuum, for some values of the impurity parameters. In the next step, after the preparation of an arbitrary non-equilibrium state, we observe the time evolution of the site magnetization. Relaxation properties are described by the long-time behavior, which is estimated using the stationary phase method. Absence of localized states defines an ergodic region in parameter space, where the system relaxes to a homogeneous magnetization. Out of this region, impurity levels split from the band, and localization phenomena may lead to non-ergodicity.     

Abundance of translation invariant pure states on quantum spin chains

We construct a set of translation invariant pure states of a quantum spin chain, which is w -dense in the set of all translation invariant states of the chain. Each of the approximating states has exponential decay of correlations, and is the unique ground state of a finite range Hamiltonian with a spectral gap above the ground state energy.     

Magnetic resonance in quantum spin chains

The present understanding of quantum spin chains is reviewed from the magnetic resonance point of view. This includes both the ideal one-dimensional properties in the spin sector as well as the complex interplay with orbital, charge, and lattice degrees of freedom which govern the ground state. In copper-phosphates we observe an extremely extended paramagnetic regime governed by strong antiferromagnetic correlations with record values of the ratio k_BT_N/J < 6×10⁻⁴, which compares the ordering temperature of a Néel state to the magnitude of the exchange J between neighbouring spins. A detailed quantitative discussion of NMR and ESR relaxation within this paramagnetic regime elucidates the relevant exchange interactions in typical bonding geometries of most common quantum-spin-chain systems like KCuF₃, CuGeO₃, Na_xV₂O₅, and LiCuVO₄. Concerning the ground state, paramount topics of modern solid-state physics arise among these examples as there are multiferroicity, charge order, metal-insulator transition, and spin dimerization as well as phase separation.     

Heat transport in quantum spin chains

We discuss the problem of heat conduction in quantum spin chain models. To investigate this problem it is necessary to consider the finite open system connected to heat baths. We describe two different procedures to couple the system with the reservoirs: a model of stochastic heat baths and the quantum trajectories solution of the quantum master equation. The stochastic heat bath procedure operates on the pure wave function of the isolated system, so that it is locally and periodically collapsed to a quantum state consistent with a boundary nonequilibrium state. In contrast, the quantum trajectories procedure evaluates ensemble averages in terms of the reduced density matrix operator of the system. We apply these procedures to different models of quantum spin chains and numerically show their applicability to study the heat flow.     

Measurement-based teleportation along quantum spin chains

We examine the teleportation of an unknown spin-1/2 quantum state along a quantum spin chain with an even number of sites. Our protocol, using a sequence of Bell measurements, may be viewed as an iterated version of the 2-qubit protocol of C. H. Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)]. A decomposition of the Hilbert space of the spin chain into 4 vector spaces, called Bell subspaces, is given. It is established that any state from a Bell subspace may be used as a channel to perform unit fidelity teleportation. The space of all spin-0 many-body states, which includes the ground states of many known antiferromagnetic systems, belongs to a common Bell subspace. A channel-dependent teleportation parameter [symbol: see text] is introduced, and a bound on the teleportation fidelity is given in terms of [symbol: see text].     

Entangled finitely correlated quantum spin chains

We study the multipartite entanglement properties of translation-invariant states of infinite quantum spin chains with a valence-bond structure.     

Spin structure factors and valence-bond-solid states of the trimerized Heisenberg chains in a magnetic field

By means of the density matrix renormalization group (DMRG) method, the static spin structure factors and the magnetization plateaus of the trimerized Heisenberg ferromagnet-ferromagnet-antiferromagnet and antiferromagnet-antiferromagnet-ferromagnet spin chains in the presence of a magnetic field are elaborately studied. It is found that in the plateau states, the static structure factor with three peaks does not vary with the external magnetic field as well as the exchange couplings; the spin correlation function behaves as a perfect sequence and has a simple relation with the magnetization per site. An approximate wave function for the plateau states is proposed, and a picture based on the valence-bond-solid states is presented in order to understand the origin and the total number of the magnetization plateaus, which are shown to be in agreement with the DMRG results.     

Using single quantum states as spin filters to study spin polarization in ferromagnets

By measuring electron tunneling between a ferromagnet and individual energy levels in an aluminum quantum dot, we show how spin-resolved quantum states can be used as filters to determine spin-dependent tunneling rates. We also observe magnetic-field-dependent shifts in the magnet's electrochemical potential relative to the dot's energy levels. The shifts vary between samples and are generally smaller than expected from the magnet's spin-polarized density of states. We suggest that they are affected by field-dependent charge redistribution at the magnetic interface.     

Low temperature thermodynamics of quantum spin chains

Low temperature thermodynamic quantities of quantum spin chains are obtained by combining the high temperature expansion and an argument based on the spin wave theory. The method is tested in the XY chain and applied to the Heisenberg chain for which low temperature specific heat and antiferromagnetic susceptibility are calculated.     

Low-energy properties of aperiodic quantum spin chains

We investigate the low-energy properties of antiferromagnetic quantum XXZ spin chains with couplings following two-letter aperiodic sequences, by an adaptation of the Ma-Dasgupta-Hu renormalization-group method. For a given aperiodic sequence, we argue that, in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. As representative illustrations, we present analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations for couplings following the Fibonacci quasiperiodic structure and a binary Rudin-Shapiro sequence, whose geometrical fluctuations are similar to those induced by randomness.     

Ground states of quantum spin systems

We prove that ground states of quantum spin systems are characterized by a principle of minimum local energy and that translationally invariant ground states are characterized by the principle of minimum energy per unit volume.     

Quantum spin chains with quantum group symmetry

We consider actions of quantum groups on lattice spin systems. We show that if an action of a quantum group respects the local structure of a lattice system, it has to be an ordinary group. Even allowing weakly delocalized (quasi-local) tails of the action, we find that there are no actions of a properly quantum group commuting with lattice translations. The non-locality arises from the ordering of factors in the quantum groupC ^*-algebra, and can be made one-sided, thus allowing semi-local actions on a half chain. Under such actions, localized quantum group invariant elements remain localized. Hence the notion of interactions invariant under the quantum group and also under translations, recently studied by many authors, makes sense even though there is no global action of the quantum group. We consider a class of such quantum group invariant interactions with the property that there is a unique translation invariant ground state. Under weak locality assumptions, its GNS representation carries no unitary representation of the quantum group.Supported in part by NSF Grant # PHY90-19433 A02Copyright © 1995 by the authors. Faithful reproduction of this article by any means is permitted for non-commercial purposes.     

Geometric aspects of quantum spin states

A number of interesting features of the ground states of quantum spin chains are analyzed with the help of a functional integral representation of the system's equilibrium states. Methods of general applicability are introduced in the context of the SU(2S+1)-invariant quantum spin-S chains with the interaction –P ^(o), whereP ^(o) is the projection onto the singlet state of a pair of nearest neighbor spins. The phenomena discussed here include: the absence of Néel order, the possibility of dimerization, conditions for the existence of a spectral gap, and a dichotomy analogous to one found by Affleck and Lieb, stating that the systems exhibit either slow decay of correlations or translation symmetry breaking. Our representation elucidates the relation, evidence for which was found earlier, of the –P ^(o) spin-S systems with the Potts and the Fortuin-Kasteleyn random-cluster models in one more dimension. The method reveals the geometric aspects of the listed phenomena, and gives a precise sense to a picture of the ground state in which the spins are grouped into random clusters of zero total spin. E.g., within such structure the dichotomy is implied by a topological argument, and the alternatives correspond to whether, or not, the clusters are of finite mean length.Work supported in part by NSF Grant PHY-9214654.Also in the Mathematics Department.     

Robust quantum state transfer in random unpolarized spin chains

We propose and analyze a new approach for quantum state transfer between remote spin qubits. Specifically, we demonstrate that coherent quantum coupling between remote qubits can be achieved via certain classes of random, unpolarized (infinite temperature) spin chains. Our method is robust to coupling-strength disorder and does not require manipulation or control over individual spins. In principle, it can be used to attain perfect state transfer over an arbitrarily long range via purely Hamiltonian evolution and may be particularly applicable in a solid-state quantum information processor. As an example, we demonstrate that it can be used to attain strong coherent coupling between nitrogen-vacancy centers separated by micrometer distances at room temperature. Realistic imperfections and decoherence effects are analyzed.