Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1003.4204

Disorder from disorder and confinement in the quantum Ising model in the pyrochlore lattice

Chyh-Hong Chern, Liao, Chen-Nan, Yang-Zhi Chou

Published Mar 22, 2010• 0 citations
arXivHTMLPDF

Abstract

At zero temperature, the classical antiferromagnetic Ising model on the pyrochlore lattice is a spin disorder phase of the critical spin correlation. It is a deconfined phase in that the binding energy of the monopole-anti-monopole pair is independent of their distance of separation. We show that turning on a transverse magnetic field turns it into the cooperative paramagnet, and the spin correlation becomes exponential decay. Furthermore, it introduces the quantum confinement (of magnetic monopoles), where the binding energy of the pair is proportional to their distance of separation. This disorder state undergoes adiabatic transition to the paramagnetic state in the large field limit. The effective Hamiltonian (without magnetic monopoles) in small field is the Ising Hamiltonian plus ring exchange interaction.

DOI
10.48550/arxiv.1003.4204

Related papers

Spin structure factor and thermodynamics in the antiferromagnetic transverse-field Ising model on the pyrochlore lattice

Cheng-Ju Lin, Chen-Nan Liao, Chyh-Hong Chern

We numerically compute the temperature dependence of the spin structure factor and thermodynamic quantities in the antiferromagnetic transverse-field Ising model in the pyrochlore lattice. This model exhibits a spin disorder ground state with exponentially decayed spin correlation. There is a pinch point structure in the spin structure factor which exhibits singular behavior at zero temperature. The residual entropy at zero temperature is also correctly obtained.

arXiv:1111.2086•Physical Review B•Apr 20, 2012•5 citations

Order, disorder, and monopole confinement in the spin- 12 XXZ model on a pyrochlore tube

Chunhan Feng, Alexander Wietek, Edwin Miles Stoudenmire +1 more

We study the ground state and thermodynamic properties of the spin-half XXZ model, with an Ising interaction ${J}_{z}$ and a transverse exchange interaction ${J}_{x}$, on a pyrochlore tube obtained by joining together elementary cubes in a one-dimensional array. Periodic boundary conditions in the transverse directions ensure that the bulk of the system consists of corner-sharing tetrahedra, with the same local geometry as the pyrochlore lattice. We use exact diagonalization, the density matrix renormalization group (DMRG), and minimally entangled typical thermal states (METTS) methods to study the system. When ${J}_{z}$ is antiferromagnetic (${J}_{z}>0$) and ${J}_{x}$ is ferromagnetic (${J}_{x}<0$), we find a transition from a spin liquid to an XY ferromagnet, which has power-law correlations at $T=0$. For ${J}_{z}<0$ and ${J}_{x}>0$, spin-two excitations are found to have lower energy than spin-one at the transition away from the fully polarized state, showing evidence for incipient spin-nematic order. When both interactions are antiferromagnetic, we find a nondegenerate ground state with no broken symmetries and a robust energy gap. The low-energy spectra evolve smoothly from predominantly Ising to predominantly XY interactions. In the spin-liquid regime of small $|{J}_{x}|$, we study the confinement of monopole-antimonopole pairs and find that the confinement length scale is larger for ${J}_{x}<0$ than for ${J}_{x}>0$, although both length scales are very short. These results are consistent with a local spin-liquid phase for the Heisenberg antiferromagnet with no broken symmetries.

arXiv:2203.00032•Physical review. B./Physical review. B•Aug 18, 2022•4 citations

Phase diagram of the XXZ pyrochlore model from pseudo-Majorana functional renormalization group

Yannik Schaden, M. G. Gonzalez, Johannes Reuther

We calculate the magnetic phase diagram of the spin- 1 / 2 nearest neighbor XXZ pyrochlore model using the pseudo-Majorana functional renormalization group in the temperature flow formalism. Our phase diagram as a function of temperature and coupling ratio, allowing both longitudinal and transverse couplings to be ferromagnetic and antiferromagnetic, reveals a large nonmagnetic regime at low temperatures, which includes the quantum spin ice phase near the antiferromagnetic Ising model, as well as the antiferromagnetic Heisenberg and XY models. We are able to detect magnetic phase transitions via critical finite size scaling down to temperatures two orders of magnitude smaller than the spin interactions, demonstrating the remarkably good performance of our method upon approaching the ground state. Specifically, the low-temperature transition from the zero-flux quantum spin ice phase into the transverse ferromagnetic phase shows very good agreement with previous quantum Monte Carlo results. Comparing our findings with classical results, we identify a quantum order-by-disorder effect near the antiferromagnetic XY model. In magnetically disordered regimes, we find characteristic patterns of broadened pinch points in the spin structure factor and investigate their evolution when approaching magnetically ordered phases. We also compute linear responses to lattice symmetry breaking perturbations and identify a possible lattice nematic ground state of the antiferromagnetic XY model.

Physical review. B./Physical review. B•Apr 24, 2025•2 citations

Phase diagram of the XXZ pyrochlore model from pseudo-Majorana functional renormalization group

Yannik Schaden, M. G. Gonzalez, Johannes Reuther

We calculate the magnetic phase diagram of the spin-$1/2$ nearest neighbor XXZ pyrochlore model using the pseudo-Majorana functional renormalization group in the temperature flow formalism. Our phase diagram as a function of temperature and coupling ratio, allowing both longitudinal and transverse couplings to be ferromagnetic and antiferromagnetic, reveals a large non-magnetic regime at low temperatures, which includes the quantum spin ice phase near the antiferromagnetic Ising model, as well as the antiferromagnetic Heisenberg and XY models. We are able to detect magnetic phase transitions via critical finite size scaling down to temperatures two orders of magnitude smaller than the spin interactions, demonstrating the remarkably good performance of our method upon approaching the ground state. Specifically, the low temperature transition from the zero-flux quantum spin ice phase into the transverse ferromagnetic phase shows very good agreement with previous quantum Monte Carlo results. Comparing our findings with classical results, we identify a quantum order-by-disorder effect near the antiferromagnetic XY model. In magnetically disordered regimes, we find characteristic patterns of broadened pinch points in the spin structure factor and investigate their evolution when approaching magnetically ordered phases. We also compute linear responses to lattice symmetry breaking perturbations and identify a possible lattice nematic ground state of the antiferromagnetic XY model.

arXiv:2412.14773•Dec 19, 2024•1 citation

Confinement, reduced entanglement, and spin-glass order in a random quantum spin-ice model

Anirudha Menon, Tom Pardini, Rajiv R. P. Singh

We study an effective spin model derived perturbatively from a random transverse-field Ising model on the pyrochlore lattice. The model consists of spin configurations on the pyrochlore lattice, restricted to the spin-ice subspace, with spins interacting with random Ising exchange couplings as well as ring exchanges along the hexagons of the lattice. This model is studied by exact diagonalization up to $N=64$ site systems. We calculate spin-glass correlation functions and local entanglement entropy ${S}_{T}$ between spins in a single tetrahedron and the rest of the system. We find that the model undergoes two phase transitions. At weak randomness the model is in a quantum spin-ice phase where ${S}_{T}=ln6$. Increasing randomness, at low transverse fields, first leads to a frozen phase, with long-range spin-glass order and ${S}_{T}=ln2$ corresponding to the Cat states associated with Ising order. Further increase in randomness leads to a random resonating-hexagon phase with a frozen backbone of spins and a broad distribution of entanglement entropies. The implications of these studies for non-Kramers rare-earth pyrochlores are discussed.

arXiv:1911.10243•Physical review. B./Physical review. B•May 21, 2020•2 citations

Transverse field Ising model on the checkerboard lattice: a plaquette-operator approach

M. Sadrzadeh, A. Langari

We study the effect of quantum fluctuations by means of a transverse magnetic field ($\Gamma$) on the antiferromagnetic $J_1-J_2$ Ising model on the checkerboard lattice, the two dimensional version of pyrochlore lattice. A plaquette operator formalism has been implemented to bosonise the model, in which a single boson is associated to each eigenstate of a plaquette and the inter-plaquette interactions define an effective Hamiltonian. The excitations of a plaquette would represent an-harmonic fluctuations of the model, which lead not only to lower the excitation energy compared with a single-spin flip but also to lift the extensive degeneracy in favor of a plaquette ordered state, which breaks lattice rotational symmetry for $J_2>J_1$ (the collinear phase). The bosonic excitation gap vanishes at the critical boundary to N\'{e}el ($J_2 J_1$) phases, respectively. At the homogeneous coupling ($J_1=J_2$) a (canted) resonating plaquette state (RPS) is established from an-harmonic fluctuations, which lasts for low fields, $\Gamma/J_1\lesssim 0.4$, followed by a crossover to the fully polarized phase. We will show that our results predict an order-by-disorder as a results of transverse field at the critical point ($J_2=0.5 J_1$) of the antiferromagnetic $J_1-J_2$ Ising square lattice.

•May 6, 2014•0 citations
At zero temperature, the classical antiferromagnetic Ising model on the pyrochlore lattice is a spin disorder phase of the critical spin correlation. It is a deconfined phase in that the binding energy of the monopole-anti-monopole pair is independent of their distance of separation. We show that turning on a transverse magnetic field turns it into the cooperative paramagnet, and the spin correlation becomes exponential decay. Furthermore, it introduces the quantum confinement (of magnetic monopoles), where the binding energy of the pair is proportional to their distance of separation. This disorder state undergoes adiabatic transition to the paramagnetic state in the large field limit. The effective Hamiltonian (without magnetic monopoles) in small field is the Ising Hamiltonian plus ring exchange interaction.
We study the ground state and thermodynamic properties of the spin-half XXZ model, with an Ising interaction Jz{J}_{z}Jz​ and a transverse exchange interaction Jx{J}_{x}Jx​, on a pyrochlore tube obtained by joining together elementary cubes in a one-dimensional array. Periodic boundary conditions in the transverse directions ensure that the bulk of the system consists of corner-sharing tetrahedra, with the same local geometry as the pyrochlore lattice. We use exact diagonalization, the density matrix renormalization group (DMRG), and minimally entangled typical thermal states (METTS) methods to study the system. When Jz{J}_{z}Jz​ is antiferromagnetic (Jz>0{J}_{z}>0Jz​>0) and Jx{J}_{x}Jx​ is ferromagnetic (Jx<0{J}_{x}<0Jx​<0), we find a transition from a spin liquid to an XY ferromagnet, which has power-law correlations at T=0T=0T=0. For Jz<0{J}_{z}<0Jz​<0 and Jx>0{J}_{x}>0Jx​>0, spin-two excitations are found to have lower energy than spin-one at the transition away from the fully polarized state, showing evidence for incipient spin-nematic order. When both interactions are antiferromagnetic, we find a nondegenerate ground state with no broken symmetries and a robust energy gap. The low-energy spectra evolve smoothly from predominantly Ising to predominantly XY interactions. In the spin-liquid regime of small ∣Jx∣|{J}_{x}|∣Jx​∣, we study the confinement of monopole-antimonopole pairs and find that the confinement length scale is larger for Jx<0{J}_{x}<0Jx​<0 than for Jx>0{J}_{x}>0Jx​>0, although both length scales are very short. These results are consistent with a local spin-liquid phase for the Heisenberg antiferromagnet with no broken symmetries.
We calculate the magnetic phase diagram of the spin- 1 / 2 nearest neighbor XXZ pyrochlore model using the pseudo-Majorana functional renormalization group in the temperature flow formalism. Our phase diagram as a function of temperature and coupling ratio, allowing both longitudinal and transverse couplings to be ferromagnetic and antiferromagnetic, reveals a large nonmagnetic regime at low temperatures, which includes the quantum spin ice phase near the antiferromagnetic Ising model, as well as the antiferromagnetic Heisenberg and XY models. We are able to detect magnetic phase transitions via critical finite size scaling down to temperatures two orders of magnitude smaller than the spin interactions, demonstrating the remarkably good performance of our method upon approaching the ground state. Specifically, the low-temperature transition from the zero-flux quantum spin ice phase into the transverse ferromagnetic phase shows very good agreement with previous quantum Monte Carlo results. Comparing our findings with classical results, we identify a quantum order-by-disorder effect near the antiferromagnetic XY model. In magnetically disordered regimes, we find characteristic patterns of broadened pinch points in the spin structure factor and investigate their evolution when approaching magnetically ordered phases. We also compute linear responses to lattice symmetry breaking perturbations and identify a possible lattice nematic ground state of the antiferromagnetic XY model.
We calculate the magnetic phase diagram of the spin-1/21/21/2 nearest neighbor XXZ pyrochlore model using the pseudo-Majorana functional renormalization group in the temperature flow formalism. Our phase diagram as a function of temperature and coupling ratio, allowing both longitudinal and transverse couplings to be ferromagnetic and antiferromagnetic, reveals a large non-magnetic regime at low temperatures, which includes the quantum spin ice phase near the antiferromagnetic Ising model, as well as the antiferromagnetic Heisenberg and XY models. We are able to detect magnetic phase transitions via critical finite size scaling down to temperatures two orders of magnitude smaller than the spin interactions, demonstrating the remarkably good performance of our method upon approaching the ground state. Specifically, the low temperature transition from the zero-flux quantum spin ice phase into the transverse ferromagnetic phase shows very good agreement with previous quantum Monte Carlo results. Comparing our findings with classical results, we identify a quantum order-by-disorder effect near the antiferromagnetic XY model. In magnetically disordered regimes, we find characteristic patterns of broadened pinch points in the spin structure factor and investigate their evolution when approaching magnetically ordered phases. We also compute linear responses to lattice symmetry breaking perturbations and identify a possible lattice nematic ground state of the antiferromagnetic XY model.
We study an effective spin model derived perturbatively from a random transverse-field Ising model on the pyrochlore lattice. The model consists of spin configurations on the pyrochlore lattice, restricted to the spin-ice subspace, with spins interacting with random Ising exchange couplings as well as ring exchanges along the hexagons of the lattice. This model is studied by exact diagonalization up to N=64N=64N=64 site systems. We calculate spin-glass correlation functions and local entanglement entropy ST{S}_{T}ST​ between spins in a single tetrahedron and the rest of the system. We find that the model undergoes two phase transitions. At weak randomness the model is in a quantum spin-ice phase where ST=ln6{S}_{T}=ln6ST​=ln6. Increasing randomness, at low transverse fields, first leads to a frozen phase, with long-range spin-glass order and ST=ln2{S}_{T}=ln2ST​=ln2 corresponding to the Cat states associated with Ising order. Further increase in randomness leads to a random resonating-hexagon phase with a frozen backbone of spins and a broad distribution of entanglement entropies. The implications of these studies for non-Kramers rare-earth pyrochlores are discussed.
We study the effect of quantum fluctuations by means of a transverse magnetic field (Γ\GammaΓ) on the antiferromagnetic J1−J2J_1-J_2J1​−J2​ Ising model on the checkerboard lattice, the two dimensional version of pyrochlore lattice. A plaquette operator formalism has been implemented to bosonise the model, in which a single boson is associated to each eigenstate of a plaquette and the inter-plaquette interactions define an effective Hamiltonian. The excitations of a plaquette would represent an-harmonic fluctuations of the model, which lead not only to lower the excitation energy compared with a single-spin flip but also to lift the extensive degeneracy in favor of a plaquette ordered state, which breaks lattice rotational symmetry for J2>J1J_2>J_1J2​>J1​ (the collinear phase). The bosonic excitation gap vanishes at the critical boundary to N\'{e}el (J2J1J_2 J_1J2​J1​) phases, respectively. At the homogeneous coupling (J1=J2J_1=J_2J1​=J2​) a (canted) resonating plaquette state (RPS) is established from an-harmonic fluctuations, which lasts for low fields, Γ/J1≲0.4\Gamma/J_1\lesssim 0.4Γ/J1​≲0.4, followed by a crossover to the fully polarized phase. We will show that our results predict an order-by-disorder as a results of transverse field at the critical point (J2=0.5J1J_2=0.5 J_1J2​=0.5J1​) of the antiferromagnetic J1−J2J_1-J_2J1​−J2​ Ising square lattice.