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

Criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model

Yoshihiro Nishiyama

arXiv:1805.00623The European Physical Journal BApr 1, 20181 citation

Two-particle bound states and one-particle structure factor in a Heisenberg bilayer system

A. Collins, Chris J. Hamer

The $S=1/2$ Heisenberg bilayer spin model at zero temperature is studied in the dimerized phase using analytic triplet-wave expansions and dimer series expansions. The occurrence of two-triplon bound states in the $S=0$ and $S=1$ channels, and antibound states in the $S=2$ channel, is predicted by the triplet-wave theory and confirmed by series expansions. All bound states are found to vanish at or before the critical coupling separating the dimerized phase from the N\'eel phase. The critical behavior of the total and single-particle static transverse structure factors is also studied by series and found to conform with theoretical expectations. The single-particle state dominates the structure factor at all couplings.The $S=1/2$ Heisenberg bilayer spin model at zero temperature is studied in the dimerized phase using analytic triplet-wave expansions and dimer series expansions. The occurrence of two-triplon bound states in the $S=0$ and $S=1$ channels, and antibound states in the $S=2$ channel, is predicted by the triplet-wave theory and confirmed by series expansions. All bound states are found to vanish at or before the critical coupling separating the dimerized phase from the N\'eel phase. The critical behavior of the total and single-particle static transverse structure factors is also studied by series and found to conform with theoretical expectations. The single-particle state dominates the structure factor at all couplings.

arXiv:0806.0694Physical Review BAug 14, 200815 citations

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.

The

S=1/2

Heisenberg bilayer spin model at zero temperature is studied in the dimerized phase using analytic triplet-wave expansions and dimer series expansions. The occurrence of two-triplon bound states in the

S=0

and

S=1

channels, and antibound states in the

S=2

channel, is predicted by the triplet-wave theory and confirmed by series expansions. All bound states are found to vanish at or before the critical coupling separating the dimerized phase from the N\'eel phase. The critical behavior of the total and single-particle static transverse structure factors is also studied by series and found to conform with theoretical expectations. The single-particle state dominates the structure factor at all couplings.