Odd Number Of Spins Research Articles

Theory of topological spin Josephson junctions

We study the spin transport through a 1D quantum Ising-XY-Ising spin link that emulates a topological superconducting-normal-superconducting structure via Jordan-Wigner (JW) transformation. We calculate, both analytically and numerically, the spectrum of spin Andreev bound states and the resulting $\mathbb{Z}_2$ fractional spin Josephson effect (JE) pertaining to the emerging Majorana JW fermions. Deep in the topological regime, we identify an effective time-reversal symmetry that leads to $\mathbb{Z}_4$ fractional spin JE in the $\textit{presence}$ of interactions within the junction. Moreover, we uncover a hidden inversion time-reversal symmetry that protects the $\mathbb{Z}_4$ periodicity in chains with an odd number of spins, even in the $\textit{absence}$ of interactions. We also analyze the entanglement between pairs of spins by evaluating the concurrence in the presence of spin current and highlight the effects of the JW Majorana states. We propose to use a microwave cavity setup for detecting the aforementioned JEs by dispersive readout methods and show that, surprisingly, the $\mathbb{Z}_2$ periodicity is immune to $\textit{any}$ local magnetic perturbations. Our results are relevant for a plethora of spin systems, such as trapped ions, photonic lattices, electron spins in quantum dots, or magnetic impurities on surfaces.

Nonlocal behaviors of spin correlations in the Haldane-Shastry model

The nonlocal factors of spin correlations are introduced for lattice spin models. Based on this concept, we investigate the nonlocal behavior of the Haldane-Shastry model with or without ring frustration. The ground state and spin correlations of the Haldane-Shastry model are calculated for both even and odd number of spins, then the nonlocal factors can be deduced analytically. It is found that the nonlocal factor due the ring frustration is the same as the Heisenberg model.

Fractionalized Fermi liquid in a frustrated Kondo lattice model

We consider Dirac electrons on the honeycomb lattice Kondo coupled to spin-1/2 degrees of freedom on the kagome lattice. The interactions between the spins are chosen along the lines of the Balents-Fisher-Girvin model that is known to host a $\mathbb{Z}_2$ spin liquid and a ferromagnetic phase. The model is amenable to sign free auxiliary field quantum Monte Carlo simulations. While in the ferromagnetic phase the Dirac electrons acquire a gap, they remain massless in the $\mathbb{Z}_2$ spin liquid phase due to the breakdown of Kondo screening. Since our model has an odd number of spins per unit cell, this phase is a non-Fermi liquid that violates the conventional Luttinger theorem which relates the Fermi surface volume to the particle density in a Fermi liquid. This non-Fermi liquid is a specific realization of the so called fractionalized Fermi liquid proposed in the context of heavy fermions. We probe the Kondo breakdown in this non-Fermi liquid phase via conventional observables such as the spectral function, and also by studying the mutual information between the electrons and the spins.

Comb tensor networks

In this paper we propose a special type of a tree tensor network that has the geometry of a comb---a 1D backbone with finite 1D teeth projecting out from it. This tensor network is designed to provide an effective description of higher dimensional objects with special limited interactions, or, alternatively, one-dimensional systems composed of complicated zero-dimensional objects. We provide details on the best numerical procedures for the proposed network, including an algorithm for variational optimization of the wave-function as a comb tensor network, and the transformation of the comb into a matrix product state. We compare the complexity of using a comb versus alternative matrix product state representations using density matrix renormalization group (DMRG) algorithms. As an application, we study a spin-1 Heisenberg model system which has a comb geometry. In the case where the ends of the teeth are terminated by spin-1/2 spins, we find that Haldane edge states of the teeth along the backbone form a critical spin-1/2 chain, whose properties can be tuned by the coupling constant along the backbone. By adding next-nearest-neighbor interactions along the backbone, the comb can be brought into a gapped phase with a long-range dimerization along the backbone. The critical and dimerized phases are separated by a Kosterlitz-Thouless phase transition, the presence of which we confirm numerically. Finally, we show that when the teeth contain an odd number of spins and are not terminated by spin-1/2's, a special type of comb edge states emerge.

Spin excitation spectrum of high-temperature cuprate superconductors from finite cluster simulations

A cluster of spins 1/2 of a finite size can be regarded as a basic building block of a spin texture in high-temperature cuprate superconductors. If this texture has the character of a network of weakly coupled spin clusters, then spin excitation spectra of finite clusters are expected to capture the principal features of the experimental spin response. We calculate spin excitation spectra of several clusters of spins 1/2 coupled by Heisenberg interaction. We find that the calculated spectra exhibit a high degree of variability representative of the actual phenomenology of cuprates, while, at the same time, reproducing a number of important features of the experimentally measured spin response. Among such features are the spin gap, the broad peak around ≃ (40–70) meV and the sharp peak at zero frequency. The latter feature emerges due to transitions inside the ground-state multiplet of the so-called ‘uncompensated’ clusters with an odd number of spins.

Generic nearest-neighbor kagome model: XYZ and Dzyaloshinskii-Moriya couplings with comparison to the pyrochlore-lattice case

The kagome lattice is a paragon of geometrical frustration, long-studied for its association with novel ground-states including spin liquids (SLs). Many recently synthesized kagome materials feature rare-earth ions, which may be expected to exhibit highly anisotropic exchange interactions. The consequences of this combination of strong exchange anisotropy and extreme geometrical frustration are yet to be fully understood. Here, we establish a general picture of the interactions and resulting ground-states (GSs) arising from nearest neighbour exchange anisotropy on the kagome lattice. We determine a generic anisotropic exchange Hamiltonian from symmetry arguments. In the high-symmetry case where reflection in the kagome plane is a symmetry of the system, the generic nearest-neighbour Hamiltonian can be locally defined as a XYZ model with out-of-plane Dzyaloshinskii-Moriya interactions. We proceed to study its phase diagram in the classical limit, making use of an exact reformulation of the Hamiltonian in terms of irreducible representations (irreps) of the lattice symmetry group. This reformulation in terms of irreps naturally explains the three-fold mapping between SLs recently studied on kagome by the present authors [Nat Commun 7, 10297 (2016)]. In addition, a number of unusual states are stabilised in the regions where different forms of GS order compete, including a stripy phase with a local Z8 symmetry and a classical analogue of a chiral SL. This generic Hamiltonian also turns out to be a fruitful hunting ground for coexistence of different forms of magnetic order, or of order and disorder, which we find is a particular property of the kagome lattice arising from the odd number of spins per frustrated unit. These results are compared and contrasted with those obtained on the pyrochlore lattice, and connection is made with recent progress in understanding quantum models with S = 1/2

Superadiabatic quantum state transfer in spin chains

In this letter we propose a superadiabatic protocol where quantum state transfer can be achieved with arbitrarily high accuracy and minimal control across long spin chains with an odd number of spins. The quantum state transfer protocol only requires the control of the couplings between the qubits on the edge and the spin chain. We predict fidelities above 0.99 for an evolution of nanoseconds using typical spin exchange coupling values of {\mu}eV. Furthermore, by building a superadiabatic formalism on top of this protocol, we propose a effective superadiabatic protocol that retains the minimal control over the spin chain and improves the fidelity by up to 20%.

Reentrant spin-flop transition in nanomagnets

Antiferromagnetic chains with an odd number of spins are known to undergo a transition from an antiparallel to a spin-flop configuration when subjected to an increasing magnetic field. We show that in the presence of an anisotropy favoring alignment perpendicular to the field, the spin-flop state appears for both weak and strong field, the antiparallel state appearing for intermediate fields. Both transitions are second order, the configuration varying continuously with the field intensity. Such re-entrant transition is robust with respect to quantum fluctuations and it might be observed in different types of nanomagnets.

Model for spin coupling disorder effects on the susceptibility of antiferromagnetic nanochains

The temperature dependence of the static magnetic susceptibility of exchange-disordered antiferromagnetic Heisenberg spin-1/2 finite chains with an odd number of spins is investigated as a function of size and type of disorder in the exchange coupling. Two models for the exchange disorder distribution are considered. At sufficiently low temperatures each chain behaves like an isolated spin-1/2 particle. As the size of the chains increases, this analogy is lost and the chains evolve into the thermodynamic limit behavior. The present study provides a simple criterion, based on susceptibility measurements, to establish when odd-sized chains effectively simulate a single spin-1/2 particle.

Direct observation of quantum criticality in Ising spin chains

We use NMR quantum simulators to study antiferromagnetic Ising spin chains undergoing quantum phase transitions. Taking advantage of the sensitivity of the systems near criticality, we detect the critical points of the transitions using a direct measurement of the Loschmidt echo. We test our simulators for spin chains of even and odd numbers of spins, and compare the experimental results to theoretical predictions.

Kondo-Enhanced Andreev Tunneling in InAs Nanowire Quantum Dots

We report measurements of the nonlinear conductance of InAs nanowire quantum dots coupled to superconducting leads. We observe a clear alternation between odd and even occupation of the dot, with subgap peaks at |V(sd)| = Delta/e markedly stronger (weaker) than the quasiparticle tunneling peaks at |V(sd)| = 2Delta/e for odd (even) occupation. We attribute the enhanced Delta peak to an interplay between Kondo correlations and Andreev tunneling in dots with an odd number of spins, and we substantiate this interpretation by a poor man's scaling analysis.

Constants of motion in NMR spectroscopy

We present a general method for constructing a subset of the constants of motion in terms of products of spin operators. These operators are then used to give insight into the multi-spin orders comprising the quasi-equilibrium state formed under a Jeener–Broekaert sequence in small, dipolar-coupled, spin systems. We further show that constants of motion that represent single-quantum coherences are present due to the symmetry of the dipolar Hamiltonian under 180° spin rotations, and that such coherences contribute a DC component to the FID which vanishes in the absence of the flip-flop terms and is only present for spin clusters with an odd number of spins.

Magnetic susceptibility in quasi one-dimensional Ba V O : chain segmentation versus the staggered field effect

A pronounced Curie-like upturn of the magnetic susceptibility x (T) of the quasi one-dimensional spin chain compound Ba2V3O9 has been found recently [1]. Frequently this is taken as a signature for a staggered field mechanism due to the presence of g-factor anisotropy and Dzyaloshinskii-Moriya interaction. We calculate this contribution within a realistic structure of vanadium 3 d- and oxygen 2p-orbitals and conclude that this mechanism is far too small to explain experimental results. We propose that the Curie term is rather due to a segmentation of spin chains caused by broken magnetic bonds which leads to uncompensated S = ½ spins of segments with odd numbers of spins. Using the finite-temperature Lanczos method we calculate their effective moment and show that ˜ 1% of broken magnetic bonds is sufficient to reproduce the anomalous low-T behavior of x(T) in Ba2V3O9.

Ground-state properties of antiferromagnetic Heisenberg spin rings

Exact ground-state properties of antiferromagnetic Heisenberg spin rings with isotropic next-neighbor interaction are presented for various numbers of spin sites and spin quantum numbers. Earlier work by Peierls, Marshall, Leib, Schultz and Mattis focused on bipartite lattices and is not applicable to rings with an odd number of spins. With the help of exact diagonalization methods we find a more general systematic behavior which for instance relates the number of spin sites and the individual spin quantum numbers to the degeneracy of the ground state. These numerical findings all comply with rigorous proofs in the cases where a general analysis could be carried out. Therefore, it can be plausibly conjectured that the ascertained properties hold for ground states of arbitrary antiferromagnetic Heisenberg spin rings.

IMPURITY BOND EFFECT ON THE ANTIFERROMAGNETIC ISING-LIKE CHAIN

We investigate the effect of an impurity bond on low-lying excited states of the antiferromagnetic Ising-like chain in terms of domain-wall excitations, using an analytical method and a numerical method. The fundamental difference between the chains with even and odd numbers of spins is discussed.

Quantum Antiferromagnetic Spin 1/2 on the Kagomté Lattice

A quantum antiferromagnetic system on the Kagomé net with periodic boundary conditions is studied using numerical diagonalization techniques. We study clusters of sizes 9, 12, 15, 18, 21 spins (see Fig. 1), which has been used in a similar study in Ref. [1]. We found that the lowest excitations are not the usually expected spin flipping excitations. The smooth decrease of the excitation energy with the increase of system sizes indicates the existence of soft modes in the thermodynamic limit. For systems with odd number of spins, the ground states are multiply degenerate. The number of degeneracy is twice that of the classical planar model.

Magnetic behaviour of spin 1/2 finite chains intercalated into graphite. Example of the copper chloroaluminate complex

New chloroaluminate compounds with copper and cobalt have been prepared and intercalated into graphite. For the copper intercalated compound X ray analysis shows a chain structure. The magnetic properties are consistent with a model of finite chain distribution of spin 1/2 Cu 2+ ions. The contribution to the susceptibility of the short chains containing an odd number of spins is a paramagnetic-like tail which is dominant at low temperatures

Nonexistence of spontaneous magnetization in Ising models with multiple-spin interactions at high temperatures

A proof is presented to show that there exists no spontaneous magnetization at high temperatures for the Ising model on the square lattice when the interactions are between nearest-neighbour pairs as well as between quartets on the basic plaquettes. The proof can be extended to the general Ising model where the interactions are short-ranged and only between even numbers of spins, and also to the Ising models for which there exist interactions between an odd number of spins, if the Hamiltonian is such that for no product of its terms the power of the spin variable is odd for only one site, when the terms of the external field are discarded.

Optical Rotation of Time‐Reversal Degenerate States

AbstractIt is shown that time‐reversal (doubly‐) degenerate, many‐electron states in molecules of point‐group symmetry C3, C4, C6, S4, and S6 and T etc., can have non‐vanishing matrix elements over a time‐odd (electric dipole‐electric dipole) polarizability operator contributing to optical rotation. In agreement with well‐known results for Kramers' doublets, the optical rotations of the two separated and oriented states of this doublet have opposite signs in this polarizability mechanism, and they have the same sign in the time‐even pseudoscalar mechanism which is the usual natural optical rotation of chiral molecules. These results are proven, in an alternative formulation using time‐reversal in a second‐order process, to hold regardless of even or odd numbers of spins—in contrast to the first‐order processes such as the Jahn‐Teller effect. The universality of time‐reversal in spin, orbital and rotational angular momentum, in point and continuous groups, is show in a unified treatment with consistent phases. It was shown also how time‐reversal symmetry can resolve the ambiguities in lower point‐groups and determine relationships for which the point‐group symmetry is powerless.

Thermodynamics of diluteXYquantum chains

It is shown that the specific heat and susceptibility (${\ensuremath{\chi}}^{\mathrm{zz}}$) of the dilute $\mathrm{XY}$ $\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}\ensuremath{-}\frac{1}{2}$ chain can be calculated by summing over the finite segments. At low temperatures the specific heat is determined by segments with an even number of spins, whereas the susceptibility is determined by segments with an odd number of spins. At low temperatures the specific heat behaves as ${(\frac{{T}_{0}}{T})}^{\frac{5}{4}}\mathrm{exp}[\ensuremath{-}2{(\frac{{T}_{0}}{T})}^{\frac{1}{2}}]$, where ${T}_{0}$ is a characteristic temperature in the dilute spin system.