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arXiv:2010.13353 · Communications Physics

Resonating dimer–monomer liquid state in a magnetization plateau of a spin-$$\frac{1}{2}$$ kagome-strip Heisenberg chain

Katsuhiro Morita, Shigetoshi Sota, Takami Tohyama

Published Jul 15, 2021• 10 citations
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Abstract

Abstract Highly frustrated spin systems such as the kagome lattice are a treasure trove of new quantum states with large entanglements. Herein, we study the spin- $$\frac{1}{2}$$ 1 2 Heisenberg model on a kagome-strip chain, which is a one-dimensional kagome lattice, using the density matrix renormalization group method. Calculating the central charge and entanglement spectrum for the kagome-strip chain, we find a gapless spin liquid state with doubly degenerate entanglement spectra in a 1/5 magnetization plateau. We also obtain a gapless low-lying continuum in the dynamic spin structure calculated using the dynamical density matrix renormalization group method. We then propose a resonating dimer–monomer liquid state that meets these features.

DOI
10.1038/s42005-021-00665-6

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Resonating dimer–monomer liquid state in a magnetization plateau of a spin-12\frac{1}{2}21​ kagome-strip Heisenberg chain
Abstract Highly frustrated spin systems such as the kagome lattice are a treasure trove of new quantum states with large entanglements. Herein, we study the spin- 12\frac{1}{2}21​ 1 2 Heisenberg model on a kagome-strip chain, which is a one-dimensional kagome lattice, using the density matrix renormalization group method. Calculating the central charge and entanglement spectrum for the kagome-strip chain, we find a gapless spin liquid state with doubly degenerate entanglement spectra in a 1/5 magnetization plateau. We also obtain a gapless low-lying continuum in the dynamic spin structure calculated using the dynamical density matrix renormalization group method. We then propose a resonating dimer–monomer liquid state that meets these features.
The spin-12\frac{1}{2}21​ Heisenberg model on a kagome lattice is a typical frustrated quantum spin system. The basic structure of a kagome lattice is also present in the kagome-strip lattice in one dimension, where a similar type of frustration is expected. We thus study the magnetization plateaus of the spin-12\frac{1}{2}21​ Heisenberg model on a kagome-strip chain with three-independent antiferromagnetic exchange interactions using the density-matrix renormalization-group method. In a certain range of exchange parameters, we find twelve kinds of magnetization plateaus, nine of which have magnetic structures breaking translational and/or reflection symmetry spontaneously. The structures are classified by an array of five-site unit cells with specific bond-spin correlations. In a case with a nontrivial plateau, namely a 3/10 plateau, we find long-period magnetic structure with a period of four unit cells.
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-12\frac{1}{2}21​ 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 15 magnetization-plateau phases, one of which is equivalent to the spin-1 Haldane phase.
The search for exotic quantum spin liquid states in simple yet realistic spin models remains a central challenge in the field of frustrated quantum magnetism. Here we consider the canonical nearest-neighbor kagome Heisenberg antiferromagnet restricted to a quasi-one-dimensional strip consisting entirely of corner-sharing triangles. Using large-scale density matrix renormalization group calculations, we identify in this model an extended gapless quantum phase characterized by central charge c=2c=2c=2 and power-law decaying spin and bond-energy correlations which oscillate at tunably incommensurate wave vectors. We argue that this intriguing spin liquid phase can be understood as a marginal instability of a two-band spinon Fermi surface coupled to an emergent U(1) gauge field, an interpretation which we substantiate via bosonization analysis and Monte Carlo calculations on model Gutzwiller variational wave functions. Our results represent one of the first numerical demonstrations of emergent fermionic spinons in a simple SU(2) invariant nearest-neighbor Heisenberg model beyond the strictly one-dimensional (Bethe chain) limit.
The search for exotic quantum spin liquid states in simple yet realistic spin models remains a central challenge in the field of frustrated quantum magnetism. Here we consider the canonical nearest-neighbor kagome Heisenberg antiferromagnet restricted to a quasi-one-dimensional strip consisting entirely of corner-sharing triangles. Using large-scale density matrix renormalization group calculations, we identify in this model an extended gapless quantum phase characterized by central charge c = 2 and power-law decaying spin and bond-energy correlations which oscillate at tunably incommensurate wave vectors. We argue that this intriguing spin liquid phase can be understood as a marginal instability of a two-band spinon Fermi surface coupled to an emergent U(1) gauge field, an interpretation which we substantiate via bosonization analysis and Monte Carlo calculations on model Gutzwiller variational wave functions. Our results represent one of the first numerical demonstrations of emergent fermionic spinons in a simple SU(2) invariant nearest-neighbor Heisenberg model beyond the strictly one-dimensional (Bethe chain) limit.
We investigate the quantum phases of a frustrated antiferromagnetic Heisenberg spin-1/2 model Hamiltonian on a Kagome-strip chain (KSC), a one-dimensional analogue of the Kagome lattice, and construct its phase diagram in an extended exchange parameter space. The isolated unit cell of this lattice comprises of five spin-1/2 particles, giving rise to several types of magnetic ground states in a unit cell: a spin-3/23/23/2 state as well as spin-1/21/21/2 states with and without additional degeneracies. We explore the ground state properties of the fully connected thermodynamic system using exact diagonalization and density matrix renormalization group methods, identifying several distinct quantum phases. All but one of the phases exhibit gapless spin excitations. The exception is a dimerized spin-gapped phase that covers a large part of the phase diagram and includes the uniformly exchange coupled system. We argue that this phase can be understood by perturbing around the limit of decoupled unit cells where each unit cell has six degenerate ground states. We use degenerate perturbation theory to obtain an effective Hamiltonian, a Kugel-Khomskii model with an anisotropic spin-one orbital degree of freedom, which helps explain the origin of dimerization.
We investigate the quantum phases of a frustrated antiferromagnetic Heisenberg spin-1/2 model Hamiltonian on a kagom\'e-strip chain (KSC), a one-dimensional analog of the kagom\'e lattice, and construct its phase diagram in an extended exchange-parameter space. The isolated unit cell of this lattice comprises of five spin-1/2 particles, giving rise to several types of magnetic ground states in a unit cell: a spin-3/23/23/2 state as well as spin-1/21/21/2 states with and without additional degeneracies. We explore the ground-state properties of the fully connected thermodynamic system using exact diagonalization and density matrix renormalization group methods, identifying several distinct quantum phases. All but one of the phases exhibit gapless spin excitations. The exception is a dimerized spin-gapped phase that covers a large part of the phase diagram and includes the uniformly exchange coupled system. We argue that this phase can be understood by perturbing around the limit of decoupled unit cells where each unit cell has six degenerate ground states. We use degenerate perturbation theory to obtain an effective Hamiltonian, a Kugel-Khomskii model with an anisotropic spin-one orbital degree of freedom, which helps explain the origin of dimerization.