Spin structure factors and valence-bond-solid states of the trimerized Heisenberg chains in a magnetic field

By means of the density matrix renormalization group (DMRG) method, the static spin structure factors and the magnetization plateaus of the trimerized Heisenberg ferromagnet-ferromagnet-antiferromagnet and antiferromagnet-antiferromagnet-ferromagnet spin chains in the presence of a magnetic field are elaborately studied. It is found that in the plateau states, the static structure factor with three peaks does not vary with the external magnetic field as well as the exchange couplings; the spin correlation function behaves as a perfect sequence and has a simple relation with the magnetization per site. An approximate wave function for the plateau states is proposed, and a picture based on the valence-bond-solid states is presented in order to understand the origin and the total number of the magnetization plateaus, which are shown to be in agreement with the DMRG results.Comment: 11 pages, 3 figure

Quantum phase diagram of the spin-11 J1−J2J_1-J_2 Heisenberg model on the honeycomb lattice

Strongly correlated systems with geometric frustrations can host the emergent phases of matter with unconventional properties. Here, we study the spin $S = 1$ Heisenberg model on the honeycomb lattice with the antiferromagnetic first- ($J_1$) and second-neighbor ($J_2$) interactions ($0.0 \leq J_2/J_1 \leq 0.5$) by means of density matrix renormalization group (DMRG). In the parameter regime $J_2/J_1 \lesssim 0.27$, the system sustains a N\'{e}el antiferromagnetic phase. At the large $J_2$ side $J_2/J_1 \gtrsim 0.32$, a stripe antiferromagnetic phase is found. Between the two magnetic ordered phases $0.27 \lesssim J_2/J_1 \lesssim 0.32$, we find a \textit{non-magnetic} intermediate region with a plaquette valence-bond order. Although our calculations are limited within $6$ unit-cell width on cylinder, we present evidence that this plaquette state could be a strong candidate for this non-magnetic region in the thermodynamic limit. We also briefly discuss the nature of the quantum phase transitions in the system. We gain further insight of the non-magnetic phases in the spin-$1$ system by comparing its phase diagram with the spin-$1/2$ system.Comment: 7 pages, 10 figure

Single-layer tensor network study of the Heisenberg model with chiral interactions on a kagome lattice

We study the antiferromagnetic kagome Heisenberg model with additional scalar-chiral interaction by using the infinite projected entangled-pair state (iPEPS) ansatz. We discuss in detail the implementation of optimization algorithm in the framework of the single-layer tensor network based on the corner-transfer matrix technique. Our benchmark based on the full-update algorithm shows that the single-layer algorithm is stable, which leads to the same level of accuracy as the double-layer ansatz but with much less computation time. We further apply this algorithm to study the nature of the kagome Heisenberg model with a scalar-chiral interaction by computing the bond dimension scaling of magnetization, bond energy difference, chiral order parameter and correlation length. In particular, we find that for strong chiral coupling the correlation length, which is extracted from the transfer matrix, saturates to a finite value for large bond dimension, representing a gapped spin-liquid state. Further comparison with density matrix renormalization group results supports that our iPEPS faithfully represents the time-reversal symmetry breaking chiral state. Our iPEPS simulation results shed new light on constructing PEPS for describing gapped chiral topological states.Comment: 11 pages, 7 figures, sample source codes are available at https://gitlab.com/rezah/a-single-layer-tensor-network-algorith

Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model

The fractional quantum Hall effect (FQHE) realized in two-dimensional electron systems under a magnetic field is one of the most remarkable discoveries in condensed matter physics. Interestingly, it has been proposed that FQHE can also emerge in time-reversal invariant spin systems, known as the chiral spin liquid (CSL) characterized by the topological order and the emerging of the fractionalized quasiparticles. A CSL can naturally lead to the exotic superconductivity originating from the condense of anyonic quasiparticles. Although CSL was highly sought after for more than twenty years, it had never been found in a spin isotropic Heisenberg model or related materials. By developing a density-matrix renormalization group based method for adiabatically inserting flux, we discover a FQHE in a spin-$\frac{1}{2}$ isotropic kagome Heisenberg model. We identify this FQHE state as the long-sought CSL with a uniform chiral order spontaneously breaking time reversal symmetry, which is uniquely characterized by the half-integer quantized topological Chern number protected by a robust excitation gap. The CSL is found to be at the neighbor of the previously identified $Z_2$ spin liquid, which may lead to an exotic quantum phase transition between two gapped topological spin liquids.Comment: 12 pages, 12 figures, include the Supplemental Materia

Quantum Anomalous Hall Insulator Stabilized By Competing Interactions

We study the quantum phases driven by interaction in a semimetal with a quadratic band touching at the Fermi level. By combining the density matrix renormalization group (DMRG), analytical power expanded Gibbs potential method, and the weak coupling renormalization group, we study a spinless fermion system on a checkerboard lattice at half-filling, which has a quadratic band touching in the absence of interaction. In the presence of strong nearest-neighbor ($V_1$) and next-nearest-neighbor ($V_2$) interactions, we identify a site nematic insulator phase, a stripe insulator phase, and a phase separation region, in agreement with the phase diagram obtained analytically in the strong coupling limit (i.e. in the absence of fermion hopping). In the intermediate interaction regime, we establish a quantum anomalous Hall phase in the DMRG as evidenced by the spontaneous time-reversal symmetry breaking and the appearance of a quantized Chern number $C = 1$. For weak interaction, we utilize the power expanded Gibbs potential method that treats $V_1$ and $V_2$ on equal footing, as well as the weak coupling renormalization group. Our analytical results reveal that not only the repulsive $V_1$ interaction, but also the $V_2$ interaction (both repulsive and attractive), can drive the quantum anomalous Hall phase. We also determine the phase boundary in the $V_1$-$V_2$ plane that separates the semimetal from the quantum anomalous Hall state. Finally, we show that the nematic semimetal, which was proposed for $|V_2| \gg V_1$ at weak coupling in a previous study, is absent, and the quantum anomalous Hall state is the only weak coupling instability of the spinless quadratic band touching semimetal.Comment: 25 pages, 19 figure

Magnetism and thermodynamics of spin-(1/2,1) decorated Heisenberg chain with spin-1 pendants

The magnetic and thermodynamic properties of a new ferrimagnetic decorated spin-(1/2,1) Heisenberg chain with spin-1 pendant spins are investigated for three cases: (A) J1,J2>0; (B) J1>0, J20, where J1 and J2 are the exchange couplings between spins in the chain and along the rung, respectively. The low-lying and magnetic properties are explored jointly by the real-space renormalization group, spin wave, and density-matrix renormalization group methods, while the transfer-matrix renormalization group method is invoked to study the thermodynamics. It is found that the magnon spectra consist of a gapless and two gapped branches. Two branches in case (C) have intersections. The coupling dependence of low-energy gaps are analyzed. In a magnetic field, an m=3/2 (m is the magnetization per unit cell) plateau is observed for case (A), while two plateaux at m=1/2 and 3/2 are observed for cases (B) and (C). Between the two plateaux in cases (B) and (C), the sublattice magnetizations for the spins coupled by ferromagnetic interactions have novel decreasing regions with increasing the magnetic field. At finite temperature, the zero-field susceptibility temperature product chi*T and specific heat exhibit distinct exotic features with varying the couplings and temperature for different cases. chi*T is found to converge as T approaches zero, which is different from the divergent behavior in the spin-(1/2,1) mixed-spin chain without pendants. The observed thermodynamic behaviors are also discussed with the help of their low-lying excitations.Comment: 10 pages, 8 figures, accepted by Phys. Rev.

Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice

By using Gutzwiller projected fermionic wave functions and variational Monte Carlo technique, we study the spin-$1/2$ Heisenberg model with the first-neighbor ($J_1$), second-neighbor ($J_2$), and additional scalar chiral interaction $J_{\chi}{\bf S}_i \cdot ({\bf S}_j \times {\bf S}_k)$ on the triangular lattice. In the non-magnetic phase of the $J_1-J_2$ triangular model with $0.08 \lesssim J_2/J_1 \lesssim 0.16$, recent density-matrix renormalization group (DMRG) studies [Zhu and White, Phys. Rev. B {\bf 92}, 041105 (2015); Hu, Gong, Zhu, and Sheng, Phys. Rev. B {\bf 92}, 140403 (2015)] find a possible gapped spin liquid with the signal of a competition between a chiral and a $Z_2$ spin liquid. Motivated by the DMRG results, we consider the chiral interaction $J_{\chi}{\bf S}_i \cdot ({\bf S}_j \times {\bf S}_k)$ as a pertubation for this non-magnetic phase. We find that with growing $J_{\chi}$, the gapless U(1) Dirac spin liquid, which has the best variational energy for $J_{\chi}=0$, exhibits the energy instability towards a gapped spin liquid with non-trivial magnetic fluxes and nonzero chiral order. We calculate topological Chern number and ground-state degeneracy, both of which identify this flux state as the chiral spin liquid with fractionalized Chern number $C=1/2$ and two-fold topological degeneracy. Our results indicate a positive direction to stabilize a chiral spin liquid near the non-magnetic phase of the $J_1-J_2$ triangular model.Comment: 8 pages, 7 figure

Low-energy effective theory and two distinct critical phases in a spin-1/2 frustrated three-leg spin tube

Motivated by the crystal structures of [(CuCl2tachH)3Cl]Cl2 and Ca3Co2O6, we develop a low-energy effective theory using the bosonization technique for a spin-1/2 frustrated three-leg spin tube with trigonal prism units in two limit cases. The features obtained with the effective theory are numerically elucidated by the density matrix renormalization group method. Three different quantum phases in the ground state of the system, say, one gapped dimerized phase and two distinct gapless phases, are identified, where the two gapless phases are found to have the conformal central charge c=1 and 3/2, respectively. Spin gaps, spin and dimer correlation functions, and the entanglement entropy are obtained. In particular, it is disclosed that the critical phase with c=3/2 is the consequence of spin frustrations, which might belong to the SU(2)k=2 Wess-Zumino-Witten-Novikov universality class, and is induced by the twist term in the bosonized Hamiltonian density.Comment: 5 pages, 6 figure

Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagom\'e Lattice

We study the quantum phase diagram of the spin-$1/2$ Heisenberg model on the kagom\'e lattice with first-, second-, and third-neighbor interactions $J_1$, $J_2$, and $J_3$ by means of density matrix renormalization group. For small $J_2$ and $J_3$, this model sustains a time-reversal invariant quantum spin liquid phase. With increasing $J_2$ and $J_3$, we find in addition a $q=(0,0)$ N\'{e}el phase, a chiral spin liquid phase, a valence-bond crystal phase, and a complex non-coplanar magnetically ordered state with spins forming the vertices of a cuboctahedron known as a cuboc1 phase. Both the chiral spin liquid and cuboc1 phase break time reversal symmetry in the sense of spontaneous scalar spin chirality. We show that the chiralities in the chiral spin liquid and cuboc1 are distinct, and that these two states are separated by a strong first order phase transition. The transitions from the chiral spin liquid to both the $q=(0,0)$ phase and to time-reversal symmetric spin liquid, however, are consistent with continuous quantum phase transitions.Comment: 8 pages, 8 figure

Possible Nematic Spin Liquid in Spin-11 Antiferromagnetic System on the Square Lattice: Implication for the Nematic Paramagnetic State of FeSe

The exotic normal state of iron chalcogenide superconductor FeSe, which exhibits vanishing magnetic order and possesses an electronic nematic order, triggered extensive explorations of its magnetic ground state. To understand its novel properties, we study the ground state of a highly frustrated spin-$1$ system with bilinear-biquadratic interactions using unbiased large-scale density matrix renormalization group. Remarkably, with increasing biquadratic interactions, we find a paramagnetic phase between N\'eel and stripe magnetic ordered phases. We identify this phase as a candidate of nematic quantum spin liquid by the compelling evidences, including vanished spin and quadrupolar orders, absence of lattice translational symmetry breaking, and a persistent non-zero lattice nematic order in the thermodynamic limit. The established quantum phase diagram natually explains the observations of enhanced spin fluctuations of FeSe in neutron scattering measurement and the phase transition with increasing pressure. This identified paramagnetic phase provides a new possibility to understand the novel properties of FeSe.Comment: 4 pages, 5 figures, with supplemental materia