Dimensional Spin Chain Research Articles

Remarks on Effects of Projective Phase on Eigenstate Thermalization Hypothesis

Abstract The existence of p-form symmetry in a (d + 1)-dimensional quantum field is known to always lead to the breakdown of the eigenstate thermalization hypothesis for certain (d − p)-dimensional operators other than symmetry operators under some assumptions. The assumptions include the mixing of symmetry sectors within a given energy shell, which is rather challenging to verify because it requires information on the eigenstates in the middle of the spectrum. We reconsider this assumption from the viewpoint of projective representations to avoid this difficulty. In the case of $\mathbb {Z}_N$ symmetries, we can circumvent the difficulty by considering $\mathbb {Z}_N\times \mathbb {Z}_N$-symmetric theories with nontrivial projective phases, and perturbing the Hamiltonian while preserving one of the $\mathbb {Z}_N$ symmetries of our interest. We also perform numerical analyses for (1 + 1)-dimensional spin chains and the (2 + 1)-dimensional $\mathbb {Z}_2$ lattice gauge theory.

Field-temperature induced dimensionality crossover in Ca3Co2O6 spin system

Quasi-one dimensional spin chain compound, Ca3Co2O6, undergoes field and temperature induced dimensionality crossover at about 25 K from one-dimension to three-dimensionally correlated state. It is shown that interplay of intrachain and interchain couplings with thermal energy in this infinite spin chain system is responsible for this phenomenon. It is established from the measurement of temperature dependent magnetic susceptibility and field dependence of magnetization along different crystallographic axes of the single crystal. Further, the effect of chain truncation on dimensionality crossover has been studied to substantiate the role of these interactions in this phenomenon. Reduction of chain length causes decrease of the effective intrachain coupling strength without affecting the interaction of neighbouring chains significantly. As a result, the propensity of dimensional crossover is found to be weaker in the broken chain compared to the longer chain.

Solving the quantum dimer and six-vertex models one electric field line at a time

The nature and the very existence of the resonant plaquette valence bond state that separates the classical columnar phase and the Rokhsar and Kivelson point in the quantum dimer model remains unsettled. Here we take a different line of attack on this model, and on the closely related six vertex model, by exploiting the global conservation law of the number of electric field lines. This allows us to study a single fluctuating electric field line which we show maps exactly onto a one dimensional spin chain. In the case of the six vertex model, the electric field line maps onto the celebrated spin 1/2 XXZ model which can be solved exactly. In the quantum dimer model, the electric field line is mapped onto a two-leg spin 1/2 ladder, which we study using numerical exact diagonalization. Our findings are consistent with the existence of three distinct phases including a Luttinger liquid phase, the one-dimensional precursor to the two-dimensional plaquette valence bond solid. The uncanny resemblance of our quasi-one-dimensional electric field line problem to the full two-dimensional problem suggests that much of the behavior of the latter might be understood by thinking of it as a closely packed array of field lines which themselves are undergoing non-trivial phase transitions.

Generation of quantum states by the dynamics of spin chains: Analytical solution

We design a quasi-one dimensional spin chain with engineered coupling strengths such that the natural dynamics of the spin chain evolves a single excitation localized at the left hand site to any specified single particle state on the whole chain. Our treatment is an exact solution to a problem which has already been addressed in approximate ways. As two important examples, we study the $W$ states and Gaussian states with arbitrary width.

Entanglement entropy distribution in the strongly disordered one-dimensional Anderson mode

The entanglement entropy (EE) distribution of strongly disordered one dimensional spin chains, which are equivalent to spinless fermions at half-filling on a bond (hopping) disordered one-dimensional Anderson model, has been shown to exhibit very distinct features such as peaks at integer multiplications of , essentially counting the number of singlets traversing the boundary. Here we show that for a canonical Anderson model with box distribution on-site disorder and repulsive nearest-neighbor interactions the EE distribution also exhibits interesting features, albeit different than the distribution seen for the bond disordered Anderson model. The canonical Anderson model shows a broad peak at low entanglement values and one narrower peak at . Density matrix renormalization group calculations reveal this structure and the influence of the disorder strength and the interaction strength on its shape. A modified real space renormalization group method was used to get a better understanding of this behavior. As might be expected the peak centered at low values of EE has a tendency to shift to lower values as disorder is enhanced. A second peak appears around the EE value of , this peak is broadened and no additional peaks at higher integer multiplications of are seen. We attribute the differences in the distribution between the canonical model and the broad hopping disorder to the influence of the on-site disorder which breaks the symmetry across the boundary.

Angle resolved photoemission spectroscopy study of the spin-charge separation in the strongly correlated cuprates SrCuO2 and Sr2CuO3 with S = 0 impurities

We present the results of an Angle-Resolved Photoemission Spectroscopy study on the pristine and doped quasi-one dimensional spin chains cuprates: SrCuO2, SrCu0.99M0.01O2 with (M = Mg2+ or Zn2+), Sr2CuO3 and Sr2Cu(1-x)NixO3 with (x = 0.01 or 0.02), where the dopant is a non-magnetic impurity. Both systems are quantum critical and obey the Tomonaga-Luttinger spin liquid theory. Due to low dimensionality, the separation of the degrees of freedom of the collective excitation modes of spin and charge occurs, resulting in two distinct band dispersions ascribed to spinon and holon quasi-particles, at a binding energy of about 1.2 eV. Several experimental probes show that the finite size effect, in these strongly correlated electron compounds, resulting from chains breaking by the non-magnetic impurities, has a strong impact on the ground state of their quasi-particles excitations. On the other hand, our Angle Resolved Photoemission Spectroscopy data do not show any evolution of the spinon branch upon doping, in terms of energy position at Г. We also extract the antiferromagnetic superexchange coupling and inter-site hopping constants JAF and t.

“Metamagnetoelectric” effect in multiferroics

We present a theoretical calculation of magnetoelectric properties in a quasi-two dimensional spin chain externally controlled by a static electric field in y-direction and magnetic field in z-direction. Given the diversity of properties in functional materials and their applications in physics, the multiferroic model is investigated. By using the Fermi–Dirac statistics of quantum gases and the Landau theory, we assess the effects of the Dzyaloshinskii-Moriya interaction and the electric polarization on the magnetoelectric coupling that induces at low temperature the “metamagnetoelectric” effet, and likewise affects the ferroelectricity induced through symmetry mechanisms and magnetic properties of the multiferroic system. In fact, the variation of the induced polarisation due to spin arrangement through the Dzyaloshinskii-Moriya interaction gives rise to a multistep interdependent metamagnetic and metaelectric transitions which are settled up by the corresponding Dzyaloshinskii-Moriya parameter and the system then exhibits a spin gap that results from an electric and a magnetic demagnetization field range. This metamagnetoelectric effect observed in these multiferroic materials model is seem to be highly tunable via the external electric and magnetic fields and thus can be crucial in the design of new mechanisms for the processing and storage of data and other spintronic applications.

Anderson localisation in spin chains for perfect state transfer

Anderson localisation is an important phenomenon arising in many areas of physics, and here we explore it in the context of quantum information devices. Finite dimensional spin chains have been demonstrated to be important devices for quantum information transport, and in particular can be engineered to allow for "perfect state transfer" (PST). Here we present extensive investigations of disordered PST spin chains, demonstrating spatial localisation and transport retardation effects, and relate these effects to conventional Anderson localisation. We provide thresholds for Anderson localisation in these finite quantum information systems for both the spatial and the transport domains. Finally, we consider the effect of disorder on the eigenstate and energy spectrum of our Hamiltonian, where results support our conclusions on the presence of Anderson localisation.

Excited states in spin chains from conformal blocks

We develop a method of constructing excited states in one dimensional spin chains which are derived from the $SU(2)_1$ Wess-Zumino-Witten Conformal Field Theory (CFT) using a parent Hamiltonian approach. The resulting systems are equivalent to the Haldane-Shastry model. In our ansatz, correlation functions between primary fields correspond to the ground state of the spin system, whereas excited states are obtained by insertion of descendant fields. Our construction is based on the current algebra of the CFT and emphasizes the close relation between the spectrum of the spin system and the underlying CFT. This general structure might imply that the method could be applied to a wider range of model systems.

Guided magnon transport in spin chains: Transport speed and correcting for disorder

High fidelity quantum information transport is necessary for most practical models of quantum computation. By analogy with optical wave guides, a spatio-temporally varying magnetic potential on a one dimensional spin chain can achieve high fidelity transport of spin excitations. By comparing different potential shapes, we establish the effects of potential shape on the fidelity and transport speed. We incorporate disorder into our model and show methods to minimise its effect on transport. Finally, we discuss implementations of our scheme in several accessible systems based on hydrogenic approximations.

Revisiting 2D Lattice Based Spin Flip-Flop Ising Model: Magnetic Properties of a Thin Film and Its Temperature Dependence

This paper presents a brief review of Ising’s work done in 1925 for one dimensional spin chain with periodic boundary condition. Ising observed that no phase transition occurred at finite temperature in one dimension. He erroneously generalized his views in higher dimensions but that was not true. In 1941 Kramer and Wannier obtained quantitative result for two dimensional Ising model and successfully deduced the critical temperature of the system. In 1944 Onsager explicitly obtained free energy in zero fields. Though only 1dimensional formula has been derived in this review paper but Monte Carlo simulations results verify the established part of experiment and theory and explore the temperature dependence of magnetic property of thin film in 2D case. The paramagnetic case with spin coupling coefficient J=0 and ferromagenetic cases with J=0.50, 0.75 & 1.0 are studied at temperatures kT=0.20, 0.30, 0.40, 0.50, 0.60, 1.0, 1.5 & 2.0. The change in behavior from ferro to para are also observed and explained at high T values. I have demonstrated data writing for application purpose by writing number 10 on a thin ferromagnetic tape (i.e 2D film).

Many-body localization and symmetry-protected topological order

Recent work shows that highly excited many-body localized eigenstates can exhibit broken symmetries and topological order, including in dimensions where such order would be forbidden in equilibrium. In this paper we extend this analysis to discrete symmetry protected order via the explicit examples of the Haldane phase of one dimensional spin chains and the topological Ising paramagnet in two dimensions. We comment on the challenge of extending these results to cases where the protecting symmetry is continuous.

Hydrothermally synthesized oxalate and phenanthroline based ferrimagnetic one-dimensional spin chain molecular magnets [{Fe(Δ)Fe(Λ)}1−x{Cr(Δ)Cr(Λ)}x(ox)2(phen)2]n (x = 0, 0.1 and 0.5) with giant coercivity of 3.2 Tesla

Oxalate (ox) and phenanthroline (phen) ligands based one dimensional spin chain molecular magnets, [{Fe(Δ)Fe(Λ)}1−x{Cr(Δ)Cr(Λ)}x(ox)2(phen)2]n (x = 0, 0.1, and 0.5) have been designed, and synthesized using a hydrothermal synthesis method. The Rietveld refinement of the powder X-ray and neutron diffraction patterns at room temperature confirms the single-phase formation of the compounds in the monoclinic structure with a space group P21. The compounds consist of two ligands, the oxalate (C2O42−) as a coordination acceptor building block and the neutral phen (C12H8N2) as a coordination donor building block. Both ligands are connected to Fe ions of different symmetry {Fe(Δ) and Fe(Λ)}, thus forming an alternating zigzag chain like crystal structure having the repeating unit of [phen-Fe(Δ)-C2O4-Fe(Λ)-phen]n. The chain is infinite in length and lies in the crystallographic ac plane. The interchain is well separated with an intermetallic distance of ∼8.8 Å and the absence of an interchain π–π overlap between the organic ligands, resulting in a magnetic isolation between the interchains. The Mössbauer spectroscopy reveals the presence of high spin states of the Fe2+ ions of the compound for x = 0 whereas, both high-spin Fe2+ (t2g4eg2, S = 2) as well as low spin Fe2+ (t2g6eg0, S = 0) states are present for the compounds x = 0.1 and 0.5. The dc magnetization measurements show that the compounds exhibit spontaneous magnetization below ∼9 K. The transition temperature is found to be ∼8.7, 8.2 and 4.0 K for x = 0, 0.1 and 0.5 compounds, respectively. Moreover, a short range antiferromagnetic spin–spin correlation around 18–45 K has been observed for the compounds x = 0 and 0.1. An application of the Ising chain model to the dc magnetization data reveals the presence of a one-dimensional magnetic nature of all compounds with alternately spaced magnetic Fe sites. It is observed that the different Landé g factors (3.4 and 2.8) and exchange coupling constant values (−86 and −54 K) for x = 0 at two alternating Fe sites give rise to a ferrimagnetic-like behavior of the chains. The ferrimagnetic chain like structure transforms toward antiferromagnetic with Cr doping i.e. for x = 0.1 and 0.5. A hysteresis loop with a giant coercivity (3.2 T for x = 0) has been observed at 1.6 K, indicating a hard magnet-type behavior. The frequency dependence of the peak temperature in ac susceptibility vs. temperature curves for the x = 0 compound has been fitted and analyzed using the Arrhenius law as well as the power law, which exclude the possibility of a spin glass behavior. The fitted parameters (Δ/kB = 208 K and τ0 = 2.9 × 10−14 s obtained from the Arrhenius law, and τ0 = 6.1 × 10−8 s, and zν = 2.6 from the power law) show that the compound obeys the Glauber dynamics and is a real ferrimagnetic one-dimensional single chain magnet. In addition, the high pressure magnetization measurements for the x = 0 compound show an enhancement in the transition temperature from ∼8.7 to 10.7 K with increasing pressure. The observation of both a one-dimensional spin chain nature and giant coercivity (3.2 Tesla) in such compounds opens up new opportunities to design and develop low dimensional molecular chain magnets through the appropriate choice of ligands using the hydrothermal synthesis method, because the observation of magnetic hysteresis of molecular origin in single-molecule magnets is considered one of the most relevant achievements in molecular magnetism.

Detection of Entanglement in Ultracold Lattice Gases

We propose the use of quantum polarization spectroscopy for detecting multi-particle entanglement of ultracold atoms in optical lattices. This method, based on a light-matter interface employing the quantum Farady effect, allows for the non destructive measurement of spin-spin correlations. We apply it to the specific example of a one dimensional spin chain and reconstruct its phase diagram using the light signal, readily measurable in experiments with ultracold atoms. Interestingly, the same technique can be extended to detect quantum many-body entanglement in such systems.

Competing orders, nonlinear sigma models, and topological terms in quantum magnets

A number of examples have demonstrated the failure of the Landau-Ginzburg-Wilson(LGW) paradigm in describing the competing phases and phase transitions of two dimensional quantum magnets. In this paper we argue that such magnets possess field theoretic descriptions in terms of their slow fluctuating orders provided certain topological terms are included in the action. These topological terms may thus be viewed as what goes wrong within the conventional LGW thinking. The field theoretic descriptions we develop are possible alternates to the popular gauge theories of such non-LGW behavior. Examples that are studied include weakly coupled quasi-one dimensional spin chains, deconfined critical points in fully two dimensional magnets, and two component massless $QED_3$. A prominent role is played by an anisotropic O(4) non-linear sigma model in three space-time dimensions with a topological theta term. Some properties of this model are discussed. We suggest that similar sigma model descriptions might exist for fermionic algebraic spin liquid phases.

Mobility of Bloch walls via the collective coordinate method

We have studied the problem of the dissipative motion of Bloch walls considering a totally anisotropic one dimensional spin chain in the presence of a magnetic field. Using the so-called "collective coordinate method" we construct an effective Hamiltonian for the Bloch wall coupled to the magnetic excitations of the system. It allows us to analyze the Brownian motion of the wall in terms of the reflection coefficient of the effective potential felt by the excitations due to the existence of the wall. We find that for finite values of the external field the wall mobility is also finite. The spectrum of the potential at large fields is investigated and the dependence of the damping constant on temperature is evaluated. As a result we find the temperature and magnetic field dependence of the wall mobility.

The spin dynamics of (VO) 2P 2O 7: A Heisenberg spin ladder

Heisenberg spin ladders offer valuable insight into the behaviour of low dimensional magnetic systems, representing an intermediate stage between one dimensional spin chains and two dimensional lattices. We have studied the spin dynamics of the spin ladder material (VO) 2P 2O 7 by inelastic neutron scattering and have found that the observed scattering is broadly consistent with the excitation spectrum predicted by theoretical studies.