Quantum Heisenberg Chain Research Articles

Heisenberg spin chain with random-sign couplings

We study the 1D quantum Heisenberg chain with randomly ferromagnetic or antiferromagnetic couplings [a model previously studied by approximate strong-disorder renormalization group (RG)]. We find that, at least for sufficiently large spin S, the ground state has "spin glass" order. The spin waves on top of this state have the dynamical exponent [Formula: see text], intermediate between the values z = 1 of the antiferromagnet and z = 2 of the ferromagnet. Density matrix renormalization group (DMRG) simulations are in good agreement with the analytical results for spins S = 1 and [Formula: see text]. The case [Formula: see text] shows large finite size effects: We suggest that this case is also ordered, but with a small ordered moment.

Popcorn Drude weights from quantum symmetry

Integrable models provide emblematic examples of non-ergodic phenomena. One of their most distinguished properties are divergent zero-frequency conductivities signalled by finite Drude weights. Singular conductivities owe to long-lived quasiparticle excitations that propagate ballistically through the system without any diffraction. The case of the celebrated quantum Heisenberg chain, one of the best-studied many-body paradigms, turns out to be particularly mysterious. About a decade ago, it was found that the spin Drude weight in the critical phase of the model assumes an extraordinary, nowhere continuous, dependence on the anisotropy parameter in the shape of a ‘popcorn function’. This unprecedented discovery has been afterwards resolved at the level of the underlying deformed quantum symmetry algebra which helps explaining the erratic nature of the quasiparticle spectrum at commensurate values of interaction anisotropy. This work is devoted to the captivating phenomenon of discontinuous Drude weights, with the aim to give a broader perspective on the topic by revisiting and reconciling various perspectives from the previous studies. Moreover, it is argued that such an anomalous non-ergodic feature is not exclusive to the integrable spin chain but can be instead expected in a number of other integrable systems that arise from realizations of the quantum group , specialized to unimodular values of the quantum deformation parameter q. Our discussion is framed in the context of gapless anisotropic quantum chains of higher spin and the sine-Gordon quantum field theory in two space-time dimensions.

Dissipation-Induced Order: The S=1/2 Quantum Spin Chain Coupled to an Ohmic Bath.

We consider an S=1/2 antiferromagnetic quantum Heisenberg chain where each site is coupled to an independent bosonic bath with ohmic dissipation. The coupling to the bath preserves the global SO(3) spin symmetry. Using large-scale, approximation-free quantum MonteCarlo simulations, we show that any finite coupling to the bath suffices to stabilize long-range antiferromagnetic order. This is in stark contrast to the isolated Heisenberg chain where spontaneous breaking of the SO(3) symmetry is forbidden by the Mermin-Wagner theorem. A linear spin-wave theory analysis confirms that the memory of the bath and the concomitant retarded interaction stabilize the order. For the Heisenberg chain, the ohmic bath is a marginal perturbation so that exponentially large system sizes are required to observe long-range order at small couplings. Below this length scale, our numerics is dominated by a crossover regime where spin correlations show different power-law behaviors in space and time. We discuss the experimental relevance of this crossover phenomena.

Long-range-ordered phase in a quantum Heisenberg chain with interactions beyond nearest neighbors

Spin ensembles coupled to optical cavities provide a powerful platform for engineering synthetic quantum matter. Recently, we demonstrated that cavity mediated infinite range interactions can induce fast scrambling in a Heisenberg $XXZ$ spin chain (Phys. Rev. Research {\bf 2}, 043399 (2020)). In this work, we analyze the kaleidoscope of quantum phases that emerge in this system from the interplay of these interactions. Employing both analytical spin-wave theory as well as numerical DMRG calculations, we find that there is a large parameter regime where the continuous $U(1)$ symmetry of this model is spontaneously broken and the ground state of the system exhibits $XY$ order. This kind of symmetry breaking and the consequent long range order is forbidden for short range interacting systems by the Mermin-Wagner theorem. Intriguingly, we find that the $XY$ order can be induced by even an infinitesimally weak infinite range interaction. Furthermore, we demonstrate that in the $U(1)$ symmetry broken phase, the half chain entanglement entropy violates the area law logarithmically. Finally, we discuss a proposal to verify our predictions in state-of-the-art quantum emulators.

Generative neural samplers for the quantum Heisenberg chain.

Generative neural samplers offer a complementary approach to Monte Carlo methods for problems in statistical physics and quantum field theory. This paper tests the ability of generative neural samplers to estimate observables for real-world low-dimensional spin systems. It maps out how autoregressive models can sample configurations of a quantum Heisenberg chain via a classical approximation based on the Suzuki-Trotter transformation. We present results for energy, specific heat, and susceptibility for the isotropic XXX and the anisotropic XY chain are in good agreement with Monte Carlo results within the same approximation scheme.

Winding Up Quantum Spin Helices: How Avoided Level Crossings Exile Classical Topological Protection.

A magnetic helix can be wound into a classical Heisenberg chain by fixing one end while rotating the other one. We show that in quantum Heisenberg chains of finite length, the magnetization slips back to the trivial state beyond a finite turning angle. Avoided level crossings thus undermine classical topological protection. Yet, for special values of the axial Heisenberg anisotropy, stable spin helices form again, which are nonlocally entangled. Away from these sweet spots, spin helices can be stabilized dynamically or by dissipation. For half-integer spin chains of odd length, a spin slippage state and its Kramers partner define a qubit with a nontrivial Berry connection.

Interplay of Spin and Spatial Anisotropy in Low-Dimensional Quantum Magnets with Spin 1/2

Quantum Heisenberg chain and square lattices are important paradigms of a low-dimensional magnetism. Their ground states are determined by the strength of quantum fluctuations. Correspondingly, the ground state of a rectangular lattice interpolates between the spin liquid and the ordered collinear Néel state with the partially reduced order parameter. The diversity of additional exchange interactions offers variety of quantum models derived from the aforementioned paradigms. Besides the spatial anisotropy of the exchange coupling, controlling the lattice dimensionality and ground-state properties, the spin anisotropy (intrinsic or induced by the magnetic field) represents another important effect disturbing a rotational symmetry of the spin system. The S = 1/2 easy-axis and easy-plane XXZ models on the square lattice even for extremely weak spin anisotropies undergo Heisenberg-Ising and Heisenberg-XY crossovers, respectively, acting as precursors to the onset of the finite-temperature phase transitions within the two-dimensional Ising universality class (for the easy axis anisotropy) and a topological Berezinskii–Kosterlitz–Thouless phase transition (for the easy-plane anisotropy). Experimental realizations of the S = 1/2 two-dimensional XXZ models in bulk quantum magnets appeared only recently. Partial solutions of the problems associated with their experimental identifications are discussed and some possibilities of future investigations in quantum magnets on the square and rectangular lattice are outlined.

Topological magnon bound states in periodically modulated Heisenberg XXZ chains

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.

Reversible and Topotactic Solvent Removal in a Magnetic Ni(NCS)2 Coordination Polymer.

Reaction of Ni(NCS)2 with 4-(Boc-amino)pyridine in acetonitrile leads to the formation of a new coordination polymer with the composition Ni(NCS)2(4-(Boc-amino)pyridine)2·MeCN (1-MeCN). In the crystal structure the Ni(II) cations are linked by the anionic ligands into chains that are further connected into layers by intermolecular N-H···O hydrogen bonding. These layers are stacked and channels are formed, in which acetonitrile molecules are located. Solvent removal leads to the ansolvate 1, which shows microporosity as proven by sorption measurements. Single crystal X-ray investigations reveal that the solvent removal leads to a change in symmetry from primitive to C-centered, which is reversible and which proceeds via a topotactic reaction leaving the network intact. The magnetic properties of 1-MeCN and 1 are governed by the ferromagnetic exchange between spins of Ni(II) forming chains. The susceptibility and specific heat for such a quantum Heisenberg chain of S = 1 spins with zero-field splitting are calculated using the DMRG method and compared with the experimental results.

Algebra Solutions of Antiferromagnet-Antiferromagnet-Ferromagnet Quantum Heisenberg Chains Related to Sp(6,R) Lie Algebra

Antiferromagnet-antiferromagnet-ferromagnet (AF-AF-F) quantum Heisenberg chains in linear spin-wave frame is shown explicitly to have an su(1,2) algebraic structure, and its algebra solutions related to the Sp(6,R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(6,R)⊃U(1,2).

Thermodynamic properties of Cu3(CO3)2(OH)2 and the spin-1/2 distorted diamond Heisenberg chain

The thermodynamic properties of the spin-1/2 diamond quantum Heisenberg chain model have been investigated by means of the transfer matrix renormalization group (TMRG) method. Considering different crystal structures, by changing the interactions among different spins and the external magnetic fields, we first investigate the magnetic susceptibility, magnetization, and specific heat of the distorted diamond chain as a model of ferrimagnetic spin systems. The susceptibility and the specific heat show different features for different ferromagnetic (F) and antiferromagnetic (AF) interactions and different magnetic fields. A 1/3 magnetization plateau is observed at low temperature in a magnetization curve. Then, we discuss the theoretical mechanism of the double-peak structure of the magnetic susceptibility and the three-peak structure of the specific heat of the compound Cu3(CO3)2(OH)2, on which an elegant measurement was performed by Kikuchi et al. [Phys. Rev. Lett. 94, 227201 (2005)]. Our computed results are consistent with the main characteristics of the experimental data. Meanwhile, we find that the double-peak structure of susceptibility can be found in several different kinds of spin interactions in the diamond chain. Moreover, a three-peak behavior is observed in the TMRG results of magnetic susceptibility. In addition, we perform calculations relevant for some experiments and explain the characteristics of these materials.

Thermodynamics of spin-1∕2antiferromagnet-antiferromagnet-ferromagnet and ferromagnet-ferromagnet-antiferromagnet trimerized quantum Heisenberg chains

The magnetization process, the susceptibility and the specific heat of the spin-1/2 AF-AF-F and F-F-AF trimerized quantum Heisenberg chains have been investigated by means of the transfer matrix renormalization group (TMRG) technique as well as the modified spin-wave (MSW) theory. A magnetization plateau at $m=1/6$ for both trimerized chains is observed at low temperature. The susceptibility and the specific heat show various behaviors for different ferromagnetic and antiferromagnetic interactions and in different magnetic fields. The TMRG results of susceptibility and the specific heat can be nicely fitted by a linear superposition of double two-level systems, where two fitting equations are proposed. Three branch excitations, one gapless excitation and two gapful excitations, for both systems are found within the MSW theory. It is observed that the MSW theory captures the main characteristics of the thermodynamic behaviors at low temperatures. The TMRG results are also compared with the possible experimental data.

Magnetic properties of J–J–J′ quantum Heisenberg chains with spinS = 1/2,1, 3/2 and 2 in a magnetic field

By means of the density matrix renormalization group (DMRG) method, the magnetic properties of theJ–J–J ′ quantum Heisenbergchains with spin S = 1/2, 1, 3/2 and 2 in the ground states are investigated in the presence ofa magnetic field. Two different cases are considered. (a) WhenJ is antiferromagneticand J ′ is ferromagnetic (i.e. the AF–AF–F chain), the system is a ferrimagnet. Theplateaus of the magnetization are observed. It is found that the width of theplateaus decreases with increasing ferromagnetic coupling, and disappears whenJ ′/J passesa critical value. The saturated field is observed to be independent of the ferromagnetic coupling. (b) WhenJ is ferromagneticand J ′ is antiferromagnetic (i.e. the F–F–AF chain), the system becomes an antiferromagnet.The plateaus of the magnetization are also seen. The width of the plateausdecreases with decreasing antiferromagnetic coupling, and disappears whenJ ′/J passes a critical value. Though the ground state properties are quite different, themagnetization plateaus in both cases tend to disappear when the ferromagnetic couplingbecomes more dominant. Besides, no fundamental difference between the systems with spinhalf-integer and integer has been found.

Possible localized modes in the uniform quantum Heisenberg chains ofSr2CuO3

A model of mobile bond defects is tentatively proposed to analyze the ``anomalies'' observed on the NMR spectrum of the quantum Heisenberg chains of ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}.$ A bond defect is a local change in the exchange coupling. It results in a local alternating magnetization (LAM), which, when the defect moves, creates a flipping process of the local field seen by each nuclear spin. At low temperature, when the overlap of the LAM becomes large, the defects form a periodic structure, which extends over almost all the chains. In that regime, the density of bond defects decreases linearly with T.

Integrable Fateev–Zamolodchikov model with boundary impurities

The Fateev–Zamolodchikov model (i.e. the spin-1 XXZ quantum Heisenberg chain) with boundary impurities has been studied. The Bethe equations and the energy eigenvalue are derived. In the thermodynamic limit, the boundary energy induced by the impurities is obtained and discussed to some extent.

The ground state of an S = 1/2 distorted diamond chain - a model of Cu3Cl6(H2O)2·2H8C4SO2

We study the ground state of the model Hamiltonian of the trimerized S = 1/2 quantum Heisenberg chain Cu3Cl6(H2O)22H8C4SO2 in which a non-magnetic ground state was observed recently. This model consists of stacked trimers and has three kinds of coupling constant describing the couplings between spins: the intra-trimer coupling constant J1 and the inter-trimer coupling constants J2 and J3. All of these constants are assumed to be antiferromagnetic. By use of an analytical method and physical considerations, we show that there are three phases on the 2 - 3 plane (2J2 / J1, 3J3 / J1): the dimer phase, the spin-fluid phase and the ferrimagnetic phase. The dimer phase is caused by the frustration effect. In the dimer phase, there exists an excitation gap between the twofold-degenerate ground state and the first excited state, which explains the non-magnetic ground state observed in Cu3Cl6(H2O)2·2H8C4SO2. We also obtain the phase diagram on the 2 - 3 plane from the numerical diagonalization data for finite systems by use of the Lanczos algorithm.

Numerical renormalization-group study of spin correlations in one-dimensional random spin chains

We calculate the ground-state two-spin correlation functions of spin-1/2 quantum Heisenberg chains with random exchange couplings using the real-space renormalization group scheme. We extend the conventional scheme to take account of the contribution of local higher multiplet excitations in each decimation step. This extended scheme can provide highly accurate numerical data for large systems. The random average of staggered spin correlations of the chains with random antiferromagnetic (AF) couplings shows algebraic decay like $1/r^2$, which verifies the Fisher's analytic results. For chains with random ferromagnetic (FM) and AF couplings, the random average of generalized staggered correlations is found to decay more slowly than a power-law, in the form close to $1/\ln(r)$. The difference between the distribution functions of the spin correlations of the random AF chains and of the random FM-AF chains is also discussed.

Incommensuration in quantum antiferromagnetic chain

A dimerized quantum Heisenberg or XY antiferromagnetic chain has a gap in the spectrum. We show that a weak incommensurate modulation around a dimerized chain produces a zero temperature quantum critical point. As the incommensuration wavelength is varied, there is a transition to a modulated gapless state. The critical behaviour is in the universality class of the classical commensurate-incommensurate (Pokrovsky-Talapov) transition. An analogous metal-insulator transition can also take place for an incommensurate chain.

Density-Matrix Renormalization Group Study on an Impurity Symmetrically Coupled to a Quantum Heisenberg Chain

We calculate the impurity susceptibility for a spin-1/2 magnetic impurity symmetrically coupled to its two nearest-neighbor spins in an antiferromagnetic Heisenberg spin-1/2 chain. This is done by extending White's density-matrix renormalization group (DMRG) technique to finite temperatures. It is found that the impurity susceptibility satisfies Curie law at low temperatures, and that the Curie constant decreases rapidly with increasing coupling constant between the impurity spin and the spins in the chain. For strong couplings, a logarithmic dependence of the susceptibility on temperature emerges. The Curie law behavior agrees with the DMRG analysis at zero temperature but deviates from the prediction of conformal field theory.

On the Two-Magnon Bound States for the Quantum Heisenberg Chain with Variable Range Exchange

The spectrum of finite-difference two-magnon operator is investigated for quantum S=1/2 chain with variable range exchange of the form h(j-k)∝ sinh -2a(j-k). It is found that usual bound state appears for some values of the total pseudomomentum of two magnons as for the Heisenberg chain with nearest-neighbor spin interaction. Besides this state, a new type of bound state with oscillating wave function appears at larger values of the total pseudomomentum.