Double-layer Heisenberg antiferromagnet at finite temperature: Brueckner theory and quantum Monte Carlo simulations

Abstract

The double-layer Heisenberg antiferromagnet with intra-and inter-layer couplings J and J ⊥ exhibits a zero temperature quantum phase transition between a quantum disordered dimer phase for g > g c and a Neel phase with long range antiferromagnetic order for g < g c , where g = J ⊥ /J and g c ≈ 2.5. We consider the behavior of the system at finite temperature for g ≥ g c using two different and complementary approaches; an analytical Brueckner approximation and numerically exact quantum Monte Carlo simulations. We calculate the temperature dependent spin excitation spectrum (including the triplet gap), dynamic and static structure factors, the specific heat, and the uniform magnetic susceptibility. The agreement between the analytical and numerical approaches is excellent. For T → 0 and g → g c , our analytical results for the specific heat and the magnetic susceptibility coincide with those previously obtained within the nonlinear σ model approach for N → ∞. Our quantum Monte Carlo simulations extend to significantly lower temperatures than previously, allowing us to obtain accurate results for the asymptotic quantum critical behavior. We also obtain an improved estimate for the critical coupling: g c = 2.525 ± 0.002.

Magnetic properties and spin waves of bilayer magnets in a uniform field

“…The phase diagram (Fig 1) is adequately described; the locations of the zero-field transitions are (J /J ⊥ ) c1,2 = ±0. 25, these values are smaller in magnitude than the ones obtained by more accurate numerical and analytical methods [(J /J ⊥ ) c1 = 0.396 and (J /J ⊥ ) c2 = −0.435]. These deviations arise from the neglect of boson interactions which stabilize the singlet phase.…”

“…The quantum transitions between the singlet and the two ordered phases are of the O(3) universality class [11,12,18,23] and occur at critical ratios (J ⊥ /J ) c1,2 . For the antiferromagnetic case, quantum Monte Carlo calculations [11,12,25], series expansions [13], and the diagrammatic Brueckner approach [14] yield an order-disorder transition point of (J /J ⊥ ) c1 = 0.396. Bond-operator mean-field theory applied to the bilayer Heisenberg AF [15,16] gives a transition point of (J /J ⊥ ) c1 = 0.435.…”

“…On the theoretical side, the bilayer Heisenberg magnet has attracted a lot of interest [8,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] because it is a simple model for studying the interplay of long-range magnetic order and quantum disorder. Quantum-critical behavior associated with such a magnetic instability has been observed, e.g., in the cuprate superconductors over a wide range of doping levels and temperatures [26].…”

Jacobson generators, Fock representations and statistics of sl(n+1)

“…We demonstrate this on the example of a two-leg S = 1/2 Heisenberg spin ladder [19,75], where the Jacobson CAOs of order p = 1 appear in a natural way. The considerations below hold however for several other Heisenberg spin models (examples include lattice models with dimerization [71,4,5], two-layer Heisenberg models [6,42,74]) and more generally for any hard-core Bose model [14] with degenerated orbitals per site (as for instance in [82,44]). …”

Non-local Updates for Quantum Monte Carlo Simulations

“…The loop algorithm enabled simulations on up to one hundred times larger systems at ten times lower temperatures, allowing the accurate determination of the critical behavior at quantum phase transitions [34,35].…”