One-dimensional Quantum Spin Systems Research Articles

Efficiency of neural-network state representations of one-dimensional quantum spin systems

Neural-network state representations of quantum many-body systems are attracting great attention and more rigorous quantitative analysis of their expressibility and complexity is warranted. Our analysis of the restricted Boltzmann machine (RBM) state representation of one-dimensional (1D) quantum spin systems provides new insight into their computational complexity. We define a class of long-range-fast-decay (LRFD) RBM states with quantifiable upper bounds on truncation errors and provide numerical evidence for a large class of 1D quantum systems that may be approximated by LRFD RBMs of at most polynomial complexities. These results lead us to conjecture that the ground states of a wide range of quantum systems may be exactly represented by LRFD RBMs or a variant of them, even in cases where other state representations become less efficient. At last, we provide the relations between multiple typical state manifolds. Our work proposes a paradigm for doing complexity analysis for generic long-range RBMs which naturally yields a further classification of this manifold. This paradigm and our characterization of their nonlocal structures may pave the way for understanding the natural measure of complexity for quantum many-body states described by RBMs and are generalizable for higher-dimensional systems and deep neural-network quantum states. Published by the American Physical Society 2024

Electric field driven flat bands: Enhanced magnetoelectric and electrocaloric effects in frustrated quantum magnets

The $J_1$-$J_2$ quantum spin sawtooth chain is a paradigmatic one-dimensional frustrated quantum spin system exhibiting unconventional ground-state and finite-temperature properties. In particular, it exhibits a flat energy band of one-magnon excitations accompanied by an enhanced magnetocaloric effect for two singular ratios of the basal interactions $J_1$ and the zigzag interactions $J_2$. In our paper, we demonstrate that one can drive the spin system into a flat-band scenario by applying an appropriate electric field, thus overcoming the restriction of fine-tuned exchange couplings $J_1$ and $J_2$ and allowing one to tune more materials towards flat-band physics, that is to show a macroscopic magnetization jump when crossing the magnetic saturation field, a residual entropy at zero temperature as well as an enhanced magnetocaloric effect. While the magnetic field acts on the spin system via the ordinary Zeeman term, the coupling of an applied electric field with the spins is given by the sophisticated Katsura-Nagaosa-Balatsky (KNB) mechanism, where the electric field effectively acts as a Dzyaloshinskii-Moriya spin-spin interaction. The resulting novel features are corresponding reciprocal effects: We find a magnetization jump driven by the electric field as well as a jump of the electric polarization driven by the magnetic field, i.e.\ the system exhibits an extraordinarily strong magnetoelectric effect. Moreover, in analogy to the enhanced magnetocaloric effect the system shows an enhanced electrocaloric effect.

Variational Optimization of Continuous Matrix Product States.

Just as matrix product states represent ground states of one-dimensional quantum spin systems faithfully, continuous matrix product states (cMPS) provide faithful representations of the vacuum of interacting field theories in one spatial dimension. Unlike the quantum spin case, however, for which the density matrix renormalization group and related matrix product state algorithms provide robust algorithms for optimizing the variational states, the optimization of cMPS for systems with inhomogeneous external potentials has been problematic. We resolve this problem by constructing a piecewise linear parameterization of the underlying matrix-valued functions, which enables the calculation of the exact reduced density matrices everywhere in the system by high-order Taylor expansions. This turns the variational cMPS problem into a variational algorithm from which both the energy and its backwards derivative can be calculated exactly and at a cost that scales as the cube of the bond dimension. We illustrate this by finding ground states of interacting bosons in external potentials and by calculating boundary or Casimir energy corrections of continuous many-body systems with open boundary conditions.

Magnetic phase diagrams of the spin- 12 Heisenberg model on a kagome-strip chain: Emergence of a Haldane phase

Frustrated one-dimensional quantum spin systems are known to exhibit a variety of quantum ground states due to the effects of quantum fluctuations and frustrations. In a spin-1/2 kagome-strip chain, which is one of the frustrated one-dimensional spin systems, many quantum phases have been found. However, the magnetic phase diagrams of the kagome-strip chain under magnetic field have not been fully understood. We construct magnetic phase diagrams at 0, 1/5, 3/10, 1/3, 2/5, 7/15, 3/5, and 4/5 magnetization ratio in the kagome-strip chain and investigate magnetic properties in each phase using the density matrix renormalization group method. We find fifteen magnetization-plateau phases, one of which is equivalent to the spin-1 Haldane phase.

Quantized edge magnetizations and their symmetry protection in one-dimensional quantum spin systems

The bulk electric polarization works as a nonlocal order parameter that characterizes topological quantum matters. Motivated by a recent paper [H. Watanabe \textit{et al.}, Phys. Rev. B {\bf 103}, 134430 (2021)], we discuss magnetic analogs of the bulk polarization in one-dimensional quantum spin systems, that is, quantized magnetizations on the edges of one-dimensional quantum spin systems.The edge magnetization shares the topological origin with the fractional edge state of the topological odd-spin Haldane phases. Despite this topological origin, the edge magnetization can also appear in topologically trivial quantum phases. We develop straightforward field theoretical arguments that explain the characteristic properties of the edge magnetization. The field theory shows that a U(1) spin-rotation symmetry and a site-centered or bond-centered inversion symmetry protect the quantization of the edge magnetization. We proceed to discussions that quantum phases on nonzero magnetization plateaus can also have the quantized edge magnetization that deviates from the magnetization density in bulk. We demonstrate that the quantized edge magnetization distinguishes two quantum phases on a magnetization plateau separated by a quantum critical point. The edge magnetization exhibits an abrupt stepwise change from zero to $1/2$ at the quantum critical point because the quantum phase transition occurs in the presence of the symmetries protecting the quantization of the edge magnetization. We also show that the quantized edge magnetization can result from the spontaneous ferrimagnetic order.

Control of superexchange interactions with DC electric fields

We discuss DC electric-field controls of superexchange interactions. We first present generic results about antiferromagnetic and ferromagnetic superexchange interactions valid in a broad class of Mott insulators, where we also estimate typical field strength to observe DC electric-field effects: $\sim 1~\mathrm{MV/cm}$ for inorganic Mott insulators such as transition-metal oxides and $\sim 0.1~\mathrm{MV/cm}$ for organic ones. Next, we apply these results to geometrically frustrated quantum spin systems. Our theory widely applies to (quasi-)two-dimensional and thin-film systems and one-dimensional quantum spin systems on various lattices such as square, honeycomb, triangular, and kagome ones. In this paper, we give our attention to those on the square lattice and on the chain. For the square lattice, we show that DC electric fields can control a ratio of the nearest-neighbor and next-nearest-neighbor exchange interactions. In some realistic cases, DC electric fields make the two next-nearest-neighbor interactions nonequivalent and eventually turns the square-lattice quantum spin system into a deformed triangular-lattice one. For the chain, DC electric fields can induce singlet-dimer and Haldane-dimer orders. We show that the DC electric-field-induced spin gap $\propto |\boldsymbol E|^{2/3}$ in the Heisenberg antiferromagnetic chain will reach $\sim 10~\%$ of the dominant superexchange interaction in the case of a spin-chain compound $\mathrm{KCuMoO_4(OH)}$ when the DC electric field of $\sim 1~\mathrm{MV/cm}$ is applied.

Decay rates and energies of free magnons and bound states in dissipative XXZ chains

Chains of coupled two-level atoms behave as one-dimensional quantum spin systems, exhibiting free magnons and magnon bound states. While these excitations are well studied for closed systems, little consideration has been given to how they are altered by the presence of an environment. This will be especially important in systems that exhibit nonlocal dissipation, e.g., systems in which the magnons decay due to optical emission. In this paper, we consider free magnon excitations and two-magnon bound states in an XXZ chain with nonlocal dissipation. We prove that while the energy of the bound state can lie outside the two-magnon continuum of energies, the decay rate of the bound state has to always lie within the two-magnon continuum of decay rates. We then derive analytically the bound-state solutions for a system where both the XY interaction and nonlocal dissipation are nearest neighbor or next-nearest neighbor, finding that the inclusion of nonlocal dissipation allows more freedom in engineering the energy and decay rate dispersions for the bound states. Finally, we numerically study a model of an experimental setup that should allow the realization of dissipative bound states by using Rydberg-dressed atoms coupled to a photonic crystal waveguide. We demonstrate that this model can exhibit many key features of our simpler models.

Thermal density matrix renormalization group for highly frustrated quantum spin chains: A user perspective

Thermal DMRG is investigated with emphasis of employability in molecular magnetism studies. To this end magnetic observables at finite temperature are evaluated for two one-dimensional quantum spin systems: a Heisenberg chain with nearest-neighbor antiferromagnetic interaction and a frustrated sawtooth (delta) chain. It is found that thermal DMRG indeed accurately approximates magnetic observables for the chain as well as for the sawtooth chain, but in the latter case only for sufficiently high temperatures. We speculate that the reason is due to the peculiar structure of the low-energy spectrum of the sawtooth chain induced by frustration.

Bounds on the entanglement entropy of droplet states in the XXZ spin chain

We consider a class of one-dimensional quantum spin systems on the finite lattice Λ⊂Z, related to the XXZ spin chain in its Ising phase. It includes in particular the so-called droplet Hamiltonian. The entanglement entropy of energetically low-lying states over a bipartition Λ = B ∪ Bc is investigated and proven to satisfy a logarithmic bound in terms of min{n, |B|, |Bc|}, where n denotes the maximal number of down spins in the considered state. Upon addition of any (positive) random potential, the bound becomes uniformly constant on average, thereby establishing an area law. The proof is based on spectral methods: a deterministic bound on the local (many-body integrated) density of states is derived from an energetically motivated Combes–Thomas estimate.

Complex-time singularity and locality estimates for quantum lattice systems

We present and prove a well-known locality bound for the complex-time dynamics of a general class of one-dimensional quantum spin systems. Then we discuss how one might hope to extend this same procedure to higher dimensions using ideas related to the Eden growth process and lattice trees. Finally, we demonstrate with a specific family of lattice trees in the plane why this approach breaks down in dimensions greater than one and prove that there exist interactions for which the complex-time dynamics blows-up in finite imaginary time.

On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin Systems

We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems characterised by long-range interactions and with critical properties equivalent to those of the class of one-dimensional quantum systems treated by the authors in a previous publication. In particular, we use three approaches: the Trotter-Suzuki mapping, the method of coherent states, and a calculation based on commuting the quantum Hamiltonian with the transfer matrix of a classical system. This enables us to establish universality of certain critical phenomena by extension from the results in the companion paper for the classical systems identified.

Topological nature of magnetization plateaus in periodically modulated quantum spin chains

We unveil nontrivial topological properties of zero-temperature magnetization plateau states in periodically modulated quantum spin chains under a uniform magnetic field. As positions of plateaus are uniquely determined by the modulation period of exchange couplings, we find that the topologically nontrivial plateau state can be characterized by a nonzero integer Chern number and has nontrivial edge excitations. Our study clarifies the topological origin of the well-known phenomena of quantized magnetization plateaus in one-dimensional quantum spin systems and relates the plateau state to the correlated topological insulator.

Thermal Conductivity due to Spinons in the One-Dimensional Quantum Spin System Sr2V3O9

We have measured the thermal conductivity along different directions of the S = 1/2 one-dimensional (1D) spin system Sr2V3O9 in magnetic fields up to 14 T. It has been found that the thermal conductivity along the [10-1] direction, \k{appa}[10-1], is large and markedly suppressed by the application of magnetic field, indicating that there is a large contribution of spinons to \k{appa}[10-1] and that the spin chains run along the [10-1] direction. The maximum value of the thermal conductivity due to spinons is ~14 W/Km along the [10-1] direction, supporting the empirical law that the magnitude of the thermal conductivity due to spinons is roughly proportional to the antiferromagnetic interaction between the nearest neighboring spins.

Long-distance entanglement in one-dimensional quantum systems under sinusoidal deformation

We investigate entanglement generation in one-dimensional quantum spin systems with the sinusoidal deformation. In the system, the energy scale of each local term in the Hamiltonian is modified according to a position-dependent function \sin^\alpha[\frac{\pi}{N} (x - \frac{1}{2})], where x is the position of the local term and N is the length of the system. We show that at zero temperature the system with \alpha \ge 2 is able to generate a sizable entanglement between two spins at open edges even when the two spins are infinitely far apart. This long-distance entanglement is rather robust against thermal fluctuations and survives up to a temperature that decays with the system size slowly, in an algebraic form.

Study of Dynamics in Spin-1/2 Chain Using Adaptive Time-Dependent Density-Matrix Renormalization-Group Method

A numerical method of the adaptive time-dependent density-matrix renormalization-group (t-DMRG) is introduced to calculated one-dimensional quantum spin systems with next-nearest-neighbor interaction. The algorithm to study the local magnetization in spin-1/2 Heisenberg XX chain is checked. The analysis of error indicates that this method is efficient to study the spin-1/2 chain with next-nearest-neighbor interaction. By using of the method, the effects of the next-nearest-neighbor interaction on the dynamics of the local magnetization and entanglement entropy are studied.

Magnetic-field induced multiferroicity in a quantum critical frustrated spin liquid

Dielectric spectroscopy is used to check for the onset of polar order in the quasi one-dimensional quantum spin system Sul-Cu2Cl4 when passing from the spin-liquid state into the ordered spiral phase in an external magnetic field. We find clear evidence for multiferroicity in this material and treat in detail its H-T phase diagram close to the quantum-critical regime.

Ferroelectricity and New Quantum Magnetic States of Frustrated One-Dimensional Quantum Spin Systems

Ferroelectricity and New Quantum Magnetic States of Frustrated One-Dimensional Quantum Spin Systems

Tensor network techniques for the computation of dynamical observables in one-dimensional quantum spin systems

We analyze the recently developed folding algorithm (Bañuls et al 2009 Phys. Rev. Lett.102 240603) for simulating the dynamics of infinite quantum spin chains and we relate its performance to the kind of entanglement produced under the evolution of product states. We benchmark the accomplishments of this technique with respect to alternative strategies using Ising Hamiltonians with transverse and parallel fields, as well as XY models. Also, we evaluate its capability of finding ground and thermal equilibrium states.

Symmetry protection of topological phases in one-dimensional quantum spin systems

We discuss the characterization and stability of the Haldane phase in integer spin chains on the basis of simple, physical arguments. We find that an odd-$S$ Haldane phase is a topologically non-trivial phase which is protected by any one of the following three global symmetries: (i) the dihedral group of $\pi$-rotations about $x,y$ and $z$ axes; (ii) time-reversal symmetry $S^{x,y,z} \rightarrow - S^{x,y,z}$; (iii) link inversion symmetry (reflection about a bond center), consistently with previous results [Phys. Rev. B \textbf{81}, 064439 (2010)]. On the other hand, an even-$S$ Haldane phase is not topologically protected (i.e., it is indistinct from a trivial, site-factorizable phase). We show some numerical evidence that supports these claims, using concrete examples.

Heat switch effect in one-dimensional spin chains

We study heat transport in one-dimensional (1-D) quantum spin systems by the nonequilibrium Greenʼs function method. We show that, in both ferromagnetic and antiferromagnetic systems, the excitation spectrums of the reservoirs and the central spin chain can be tuned to be matched or mismatched by changing the external magnetic field. When the spectrums are matched, heat current through the system is large; however if the spectrums are mismatched, heat current becomes much smaller. Through tuning the magnetic field, the system can thus act as a heat switch, and we discuss the condition for the system to exhibit strong switch effect.