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arXiv:1602.05383 · Physical Review B

Quantum rotors on the AB2 chain with competing interactions

Antônio Sandoildo Freitas Tenório, R. R. Montenegro-Filho, Mauricio D. Coutinho-Filho

Published Aug 17, 2009• 9 citations
arXivHTMLPDF

Abstract

We present the ground-state phase diagram of $q=1/2$ quantum-rotor chains with competing interactions (frustration) calculated through cluster variational mean field approaches. We consider two interaction patterns, named ${\text{F}}_{1}$ and ${\text{F}}_{2}$ models, between the quantum-rotor momentum and position operators, which follow exchange patterns of known one-dimensional spin-1/2 systems with a ferrimagnetic state in their phase diagrams. The spin-1/2 ${\text{F}}_{1}$ model is known as the diamond chain and is related to the azurite compound, while the spin-1/2 ${\text{F}}_{2}$ model was recently shown to present a frustration-induced condensation of magnons. We provide a detailed comparison between the quantum-rotor phase diagrams, in single- and multisite mean-field approaches, and known results for the spin-1/2 models, including exact diagonalization and density matrix renormalization group data for these systems, as well as phase diagrams of the associated classical models.

DOI
10.1103/physrevb.80.054409

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We present the ground-state phase diagram of q=1/2q=1/2q=1/2 quantum-rotor chains with competing interactions (frustration) calculated through cluster variational mean field approaches. We consider two interaction patterns, named F1{\text{F}}_{1}F1​ and F2{\text{F}}_{2}F2​ models, between the quantum-rotor momentum and position operators, which follow exchange patterns of known one-dimensional spin-1/2 systems with a ferrimagnetic state in their phase diagrams. The spin-1/2 F1{\text{F}}_{1}F1​ model is known as the diamond chain and is related to the azurite compound, while the spin-1/2 F2{\text{F}}_{2}F2​ model was recently shown to present a frustration-induced condensation of magnons. We provide a detailed comparison between the quantum-rotor phase diagrams, in single- and multisite mean-field approaches, and known results for the spin-1/2 models, including exact diagonalization and density matrix renormalization group data for these systems, as well as phase diagrams of the associated classical models.
We present a brief survey of the recent theoretical work related to generic Heisenberg spin models describing quasi-one-dimensional quantum ferrimagnets.The emphasis is on quantum chains and ladders with strong competing interactions, such as the frustrated J 1 -J 2 chain with alternating (1, 1/2) spins, the spin-1/2 diamond chain with four-spin cyclic couplings, and some generic types of mixed-spin ladders with geometric frustration.As a rule, the discussed models exhibit rich quantum phase diagrams and provide some interesting examples of one-dimensional magnetic-paramagnetic quantum phase transitions.A number of open problems in the reviewed research area are discussed.
We present a brief survey of the recent theoretical work related to generic Heisenberg spin models describing quasi-one-dimensional quantum ferrimagnets. The emphasis is on quantum chains and ladders with strong competing interactions, such as the frustrated J1−J2J_1-J_2J1​−J2​ chain with alternating (1,1/2) spins, the spin-1/2 diamond chain with four-spin cyclic couplings, and some generic types of mixed-spin ladders with geometric frustration. As a rule, discussed models exhibit rich quantum phase diagrams and provide some interesting examples of one-dimensional magnetic-paramagnetic quantum phase transitions. A number of open problems in the reviewed research area are discussed.
The low-dimensional quantum spin systems have been extensively studied in the past three decades due to the novel ground states and rich magnetic behaviors,especially the quantum spin chain with diamond topology structure. Motivated by recent experimental success in Cu3(CO3)2(OH)2 compound,which is regarded as a model material of spin-1/2 diamond chain,researchers have paid a lot of attention to various variants of diamond spin chains.In this paper,we mainly examine the magnetic properties of an antisymmetric spin-1/2 Ising-Heisenberg diamond chain with the secondneighbor interaction between nodal spins.By using exact diagonalization and transfer-matrix methods,the ground-state phase diagram,magnetization behavior and macroscopic thermodynamics are exactly solved for the particular case that all magnetic bonds yield antiferromagnetic couplings,which usually shows the most interesting magnetic features closely related to a striking interplay between geometric frustration and quantum fluctuations.To clearly illustrate the effect of second-neighbor interaction item,we consider a highly frustrated situation that all Ising-Heisenberg bonds and Heisenberg bonds possess the same interaction strength.The calculation results indicate that the second-neighbor interaction item will enrich ground states and magnetization plateaus.A classical ferrimagnetic phase FRI1 corresponding to a novel two-thirds of intermediate plateau with translationally broken symmetry is introduced,manifesting itself as up-up-up-down-up-up spin configuration at a ground-state.In addition,there are other four distinct ground states which can be identified from the phase diagram,i.e.,one saturated paramagnetic phase SP,one classical ferrimagnetic phase FRI2,one quantum ferrimagnetic phase QFI and the unique quantum antiferromagnetic phase QAF.The classical phase FRI2 and quantum phase QFI both generate one-third of magnetization plateau.It is worth mentioning that all the values of these magnetization plateaus satisfy the Oshikawa-Yamanaka-Affleck condition.Besides,the results also have shown a rich variety of temperature dependence of total magnetization and specific heat.The magnetization displays the remarkable thermal-induced changes as the external field is sufficiently close to critical value where two or more than two different ground states coexist.At the critical field relevant to a coexistence of two different states,the total magnetization displays a monotonic decrease trend.The thermal dependence of zero-field specific heat displays relative complex variations for different second-neighbor interactions between nodal spins.At first,the specific heat presents only a single rounded Schottky-type maximum.Using the second-neighbor interaction,another sharp peak arises at low-temperature and is superimposed on this round maximum,and the specific heat exhibits a double-peak structure. On further strengthening,the low-temperature one keeps its height shifting towards high temperature,while the hightemperature round peak suffers great enhancement and moves in an opposite direction.Finally,the low temperature peak entirely merges with the Schottky-type peak at a certain value of second-neighbor interaction,and above this value, the specific curve recovers its single peak structure.The observed double-peak specific heat curves mainly originate from thermal excitations between the ground-state spin configuration QAF and the ones close enough in energy to the ground state.
Abstract In this work, we consider a frustrated two‐leg spin‐1/2 ladder composed of Heisenberg ferromagnetic and antiferromagnetic spin‐1/2 chains, and nearest spins from different legs interact via Heisenberg type rung exchange interactions that can be either ferromagnetic or antiferromagnetic in nature. The competing exchange interactions in the system lead to five different quantum phases like ferromagnetic, non‐collinear ferrimagnetic (NCF), , antiferromagnetic and dimer phases. The quantum phase diagram is constructed for the Heisenberg spin‐1/2 model and the phases are characterized using the correlation functions which are calculated by the density matrix renormalization group method. We also analyze the stability of phase and calculate the pitch angle in the NCF phase.
The spin-1/2 Heisenberg antiferromagnet on the frustrated diamond-decorated square lattice is known to feature various zero-field ground-state phases, consisting of extended monomer-dimer and dimer-tetramer ground states as well as a ferrimagnetic regime. Using a combination of analytical arguments, density matrix renormalization group (DMRG), exact diagonalization as well as sign-problem-free quantum Monte Carlo (QMC) calculations, we investigate the properties of this system and the related Lieb lattice in the presence of a finite magnetic field, addressing both the ground-state phase diagram as well as several thermodynamic properties. In addition to the zero-field ground states, we find at high magnetic field a spin-canted phase with a continuously rising magnetization for increasing magnetic field strength as well as the fully polarized paramagnetic phase. At intermediate field strength, we identify a first-order quantum phase transition line between the ferrimagnetic and the monomer-dimer regime. This first-order line extends to finite temperatures, terminating in a line of critical points that belong to the universality class of the two-dimensional Ising model.
The ground-state properties of the S=1/2 frustrated Heisenberg spin chain with interactions up to fourth nearest neighbors are investigated by the exact-diagonalization method and density matrix renormalization group method. Our numerical calculations clarify that the ferrimagnetic state is realized in the ground state in spite of the fact that a multi-sublattice structure in the shape of the system is absent. We find that there are two types of ferrimagnetic phases: one is the well-known ferrimagnetic phase of the Lieb-Mattis type and the other is the nontrivial ferrimagnetic phase that is different from that of the Lieb-Mattis type. Our results suggest that a multi-sublattice structure of the shape is not necessarily required for the occurrence of ferrimagnetism.