The quantum criticality and thermodynamics for the trimerized spin-1/2 isotropic XY chain with three-spin interactions in an external magnetic field are investigated by means of the Green's function theory combined with Jordan–Wigner transformation. The ground-state phase diagrams are explored, in which various phases are identified and described by typical M–h curves. Therein, two cusps emerge for strong three-spin interactions in two gapless phases at low and high fields, respectively. Moreover, the spin correlations and two-site entanglement entropy are calculated for a further understanding of quantum phase transition (QPT). It is also found that the magnetic-field-driven quantum criticality is closely related to the energy spectrum, in which an energy gap responsible for the appearance of 1/3 magnetization plateau can be opened up by three-spin interactions. The critical behavior disappears when the temperature becomes nonzero, yielding only a crossover behavior. In addition, the gapped low-lying excitations are responsible for the observed thermodynamic behaviors, wherein a structure with three peaks in the temperature dependence of specific heat is unveiled.
The quantum criticality and thermodynamics for the trimerized spin-1/2 isotropic XY chain with three-spin interactions in an external magnetic field are investigated by means of the Green's function theory combined with Jordan–Wigner transformation. The ground-state phase diagrams are explored, in which various phases are identified and described by typical M–h curves. Therein, two cusps emerge for strong three-spin interactions in two gapless phases at low and high fields, respectively. Moreover, the spin correlations and two-site entanglement entropy are calculated for a further understanding of quantum phase transition (QPT). It is also found that the magnetic-field-driven quantum criticality is closely related to the energy spectrum, in which an energy gap responsible for the appearance of 1/3 magnetization plateau can be opened up by three-spin interactions. The critical behavior disappears when the temperature becomes nonzero, yielding only a crossover behavior. In addition, the gapped low-lying excitations are responsible for the observed thermodynamic behaviors, wherein a structure with three peaks in the temperature dependence of specific heat is unveiled.
The magnetization process and elementary excitation spectra of the spin-1/2 trimerized quantum Heisenberg chain are investigated by means of Green's function theory combined with Jordan-Wigner transformation. At zero temperature, a 1/3 magnetization plateau of the system is observed. Meanwhile, we obtain the ground state phase diagram, in which the Luttinger liquid phase, the magnetization plateau state, the gapless phase and the ferromagnetic state are revealed. At finite temperatures, the magnetization behaves differently, implying the system lies in different states under different magnetic fields. It is shown that the elementary excitation spectra can unpuzzle the magnetization process. It is also found that the energy gap in the spectra is responsible for the observed 1/3 magnetization plateau.
We investigate the quantum phase transition(QPT) and magnetocaloric effect(MCE) of a tetrameric chain with three-spin interaction using Green’s function theory. The magnetization and gap analysis reveals a variety of quantum phases tuned by magnetic field and three-spin interaction, which can open up an energy gap, giving rise to the occurrence of zero magnetization plateau. However, strong three-spin couplings causing strong frustration will destroy the intermediate 1/2 plateau with emergence of a new gapless phase between two cusps. It favors achieving an enhanced MCE at the critical fields, where the minima of isoentropes as well as the valley-peak structure of Gru¨neisen ratio, signaling the accumulation of entropy, lead to cooling via adiabatic(de)magnetization processes. It is also found that the temperature dependence of specific heat combined with Gru¨neisen ratio can testify various quantum phases explicitly.
We investigate the quantum phase transition (QPT) and magnetocaloric effect (MCE) of a tetrameric chain with three-spin interaction using Green's function theory. The magnetization and gap analysis reveals a variety of quantum phases tuned by magnetic held and three-spin interaction, which can open up an energy gap, giving rise to the occurrence of zero magnetization plateau. However, strong three-spin couplings causing strong frustration will destroy the intermediate 1/2 plateau with emergence of a new gapless phase between two cusps. It favors achieving an enhanced MCE at the critical fields, where the minima of isoentropes as well as the valley-peak structure of Grüneisen ratio, signaling the accumulation of entropy, lead to cooling via adiabatic (de)magnetization processes. It is also found that the temperature dependence of specific heat combined with Grüneisen ratio can testify various quantum phases explicitly.
Critical Phases of the extended isotropic XY chain with four-spin interaction
Using the Jordan-Wigner transformation we calculate exactly the ground state and low-temperature thermodynamic properties of the spin S=1/2 isotropic XX chain with four spin interaction. In terms of the equivalent spinless fermion (SF) representation the system is viewed as a lattice fermion gas with nearest-neighbor (J) and next-next-next-neighbor (J∗/4) hopping. It is shown that with the increase of four spin coupling, at Jc∗=4J/3 the system experiences the Lifshitz type topological phase transition characterized by the tripling of Fermi points. The quantum phase transition (QPT) point marks transition from a gapless spin-liquid phase of standard XX chain into again a gapless spin-liquid phase with different character of power-low decay of spin correlations. At the transition point the free fermion dispersion relation shows flattering at Fermi points, what determines singular character of density of states ρ(ω)∼(ω/J)−2/3 and as a consequence unconventional temperature dependence of heat capacity of the system C∼(T/J∗)1/3, and singular magnetic susceptibility of the system χ(H)∼(H/J∗)−2/3. In the case of alternating magnetic field the system is characterized by the rich ground state phase diagram which contains fully polarized (ferromagnetic), gapped antiferromagnetic (AFM) and spin liquid phases. At the transition point from the gapped AFM phase into the gapless polarized spin liquid phase the system shows rapid increase of magnetization m∼(H−Hc)1/6 and magnetic susceptibility a singular behavior as χ(H)∼(H−Hc)−5/6.
Abstract Motivated by recent advancements in theoretical and experimental studies of the high-energy excitations on an antiferromagnetic trimer chain, we numerically investigate the quantum phase transition and composite dynamics in this system by applying a magnetic field. The numerical methods we used include the exact diagonalization, density matrix renormalization group, time-dependent variational principle, and cluster perturbation theory. From calculating the entanglement entropy, we have revealed the phase diagram which includes the XY-I, 1/3 magnetization plateau, XY-II, and ferromagnetic phases. Both the critical XY-I and XY-II phases are characterized by the conformal field theory with a central charge c ≃ 1. By analyzing the dynamic spin structure factor, we elucidate the distinct features of spin dynamics across different phases. In the regime with weak intertrimer interaction, we identify the intermediate-energy and high-energy modes in the XY-I and 1/3 magnetization plateau phases as internal trimer excitations, corresponding to the propagating of doublons and quartons, respectively. Notably, applying a magnetic field splits the high-energy spectrum into two branches, labeled as the upper quarton and lower quarton. Furthermore, we explore the spin dynamics of a frustrated trimerized model closely related to the quantum magnet Na 2 Cu 3 Ge 4 O 12 . In the end, we extend our discuss on the possibility of the quarton Bose-Einstein condensation in the trimer systems. Our results are expected to be further verified through the inelastic neutron scattering and resonant inelastic X-ray scattering, and also provide valuable insights for exploring high-energy exotic excitations.
The thermodynamic properties of a spin S=1/2 tetrameric Heisenberg antiferromagnetic chain with alternating interactions AF1-AF2-AF1-F (AF and F denote the antiferromagnetic and ferromagnetic couplings, respectively) are studied by means of the transfer-matrix renormalization-group method and Jordan-Wigner transformation. It is found that in the absence of magnetic field, the thermodynamic behaviors are closely related to the gapped low-lying excitations, and a novel structure with three peaks in the temperature dependence of specific heat is unveiled. In a magnetic field, a phase diagram in the temperature-field plane for the couplings satisfying JAF1=JAF2=JF is obtained, in which various phases are identified. The temperature dependence of thermodynamic quantities including the magnetization, susceptibility, and specific heat are studied to characterize the corresponding phases. It is disclosed that the magnetization has a crossover behavior at low temperature in the Luttinger liquid phase, which is shown falling into the same class as that in the S=1 Haldane chain. In the plateau regime, the thermodynamic behaviors alter at a certain field, which results from the crossing of two excitation spectra. By means of the fermion mapping, it is uncovered that the system has four spectra from fermion and hole excitations that are responsible for the observed thermodynamic behaviors.