Heisenberg Magnet in the Paramagnetic Phase: Theory.

For coupled-dimer Heisenberg magnets, a paradigm of magnetic quantum phase transitions, we develop a systematic expansion in $1/d$ , the inverse number of space dimensions. The expansion employs a formulation of the bond-operator technique and is based on the observation that a suitably chosen product-state wave function yields exact zero-temperature expectation values of local observables in the $d\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, with corrections vanishing as $1/d$ . We demonstrate the approach for a model of dimers on a hypercubic lattice, which generalizes the square-lattice bilayer Heisenberg model to arbitrary $d$ . In this paper, we use the $1/d$ expansion to calculate static and dynamic observables at zero temperature in the paramagnetic singlet phase, up to the quantum phase transition, and compare the results with numerical data available for $d=2$ . Contact is also made with previously proposed refinements of bond-operator theory as well as with a perturbative expansion in the interdimer coupling. In a companion paper, the present $1/d$ expansion will be extended to the ordered phase, where it is shown to consistently describe the entire phase diagram including the quantum critical point.For coupled-dimer Heisenberg magnets, a paradigm of magnetic quantum phase transitions, we develop a systematic expansion in $1/d$, the inverse number of space dimensions. The expansion employs a formulation of the bond-operator technique and is based on the observation that a suitably chosen product-state wave function yields exact zero-temperature expectation values of local observables in the $d\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, with corrections vanishing as $1/d$. We demonstrate the approach for a model of dimers on a hypercubic lattice, which generalizes the square-lattice bilayer Heisenberg model to arbitrary $d$. In this paper, we use the $1/d$ expansion to calculate static and dynamic observables at zero temperature in the paramagnetic singlet phase, up to the quantum phase transition, and compare the results with numerical data available for $d=2$. Contact is also made with previously proposed refinements of bond-operator theory as well as with a perturbative expansion in the interdimer coupling. In a companion paper, the present $1/d$ expansion will be extended to the ordered phase, where it is shown to consistently describe the entire phase diagram including the quantum critical point.

arXiv:1407.7870Physical Review BMar 4, 201528 citations

A coupled-mode theory of heisenberg paramagnets

Stephen William Lovesey, A. P. Megann

The European Physical Journal BDec 1, 19865 citations

Ordered magnetic phase in a frustrated spin-½ Heisenberg antiferromagnetic stacked square lattice

Zhuo Fan, Quanlin Jie

We use cluster mean-field theory, multiple block-product state, and nested cluster methods to study the ground state of a frustrated spin-\textonehalf{} Heisenberg antiferromagnetically stacked square lattice at zero temperature. By analyzing the magnetic order parameter and the geometric measure of entanglement, we find that the stacked model produces a new ordered magnetic phase because of the competition between the interlayer coupling, ${J}_{c}$ , and the frustrated interaction, ${J}_{2}$ . The interlayer coupling, ${J}_{c}$ , strengthens the long-range N\'eel phase, the new phase, and the collinear phase and destroys the disordered quantum paramagnetic (QP) phase. Increasing ${J}_{c}$ results in the new phase gradually replacing the QP phase. The QP phase disappears at the critical point ${J}_{2}^{*}$ = 0.5 and ${J}_{c}^{*}$ = 0.12.We use cluster mean-field theory, multiple block-product state, and nested cluster methods to study the ground state of a frustrated spin-\textonehalf{} Heisenberg antiferromagnetically stacked square lattice at zero temperature. By analyzing the magnetic order parameter and the geometric measure of entanglement, we find that the stacked model produces a new ordered magnetic phase because of the competition between the interlayer coupling, ${J}_{c}$, and the frustrated interaction, ${J}_{2}$. The interlayer coupling, ${J}_{c}$, strengthens the long-range N\'eel phase, the new phase, and the collinear phase and destroys the disordered quantum paramagnetic (QP) phase. Increasing ${J}_{c}$ results in the new phase gradually replacing the QP phase. The QP phase disappears at the critical point ${J}_{2}^{*}$ = 0.5 and ${J}_{c}^{*}$ = 0.12.

Physical Review BFeb 18, 20148 citations

Fluctuations in a Quantum Random Heisenberg Paramagnet

Daniel R. Grempel, Marcelo J. Rozenberg

We solve the $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ infinite-range random Heisenberg Hamiltonian in the paramagnetic phase using quantum Monte Carlo and analytical techniques. We find that the spin-glass susceptibility diverges at a finite temperature ${T}_{g}$ which demonstrates the existence of a low-temperature ordered phase. Quantum fluctuations reduce the critical temperature and the effective Curie constant with respect to their classical values. They also give rise to a redistribution of spectral weight in the dynamic structure factor in the paramagnetic phase. As the temperature decreases the spectrum of magnetic excitations gradually splits into quasielastic and inelastic contributions whose weights scale as ${S}^{2}$ and $S$ at low temperature.We solve the $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ infinite-range random Heisenberg Hamiltonian in the paramagnetic phase using quantum Monte Carlo and analytical techniques. We find that the spin-glass susceptibility diverges at a finite temperature ${T}_{g}$ which demonstrates the existence of a low-temperature ordered phase. Quantum fluctuations reduce the critical temperature and the effective Curie constant with respect to their classical values. They also give rise to a redistribution of spectral weight in the dynamic structure factor in the paramagnetic phase. As the temperature decreases the spectrum of magnetic excitations gradually splits into quasielastic and inelastic contributions whose weights scale as ${S}^{2}$ and $S$ at low temperature.

Physical Review LettersJan 12, 199870 citations

The One-dimensional Heisenberg Magnet

V. E. Korepin, N. M. Bogoliubov, Anatoli G. Izergin

Cambridge University Press eBooksAug 19, 19931 citation

For coupled-dimer Heisenberg magnets, a paradigm of magnetic quantum phase transitions, we develop a systematic expansion in

1/d

, the inverse number of space dimensions. The expansion employs a formulation of the bond-operator technique and is based on the observation that a suitably chosen product-state wave function yields exact zero-temperature expectation values of local observables in the $d\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, with corrections vanishing as

1/d

. We demonstrate the approach for a model of dimers on a hypercubic lattice, which generalizes the square-lattice bilayer Heisenberg model to arbitrary

d

. In this paper, we use the

1/d

expansion to calculate static and dynamic observables at zero temperature in the paramagnetic singlet phase, up to the quantum phase transition, and compare the results with numerical data available for

d=2

. Contact is also made with previously proposed refinements of bond-operator theory as well as with a perturbative expansion in the interdimer coupling. In a companion paper, the present

1/d

expansion will be extended to the ordered phase, where it is shown to consistently describe the entire phase diagram including the quantum critical point.

{J}_{c}

, and the frustrated interaction,

{J}_{2}

. The interlayer coupling,

{J}_{c}

, strengthens the long-range N\'eel phase, the new phase, and the collinear phase and destroys the disordered quantum paramagnetic (QP) phase. Increasing

{J}_{c}

results in the new phase gradually replacing the QP phase. The QP phase disappears at the critical point

{J}_{2}^{*}

= 0.5 and

{J}_{c}^{*}

= 0.12.

We solve the

S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2

infinite-range random Heisenberg Hamiltonian in the paramagnetic phase using quantum Monte Carlo and analytical techniques. We find that the spin-glass susceptibility diverges at a finite temperature

{T}_{g}

which demonstrates the existence of a low-temperature ordered phase. Quantum fluctuations reduce the critical temperature and the effective Curie constant with respect to their classical values. They also give rise to a redistribution of spectral weight in the dynamic structure factor in the paramagnetic phase. As the temperature decreases the spectrum of magnetic excitations gradually splits into quasielastic and inelastic contributions whose weights scale as

{S}^{2}

and

S

at low temperature.