Finite temperature line-shapes of hard-core bosons in quantum magnets: A diagrammatic approach tested in one dimension

Abstract

The dynamics in quantum magnets can often be described by effective models with bosonic excitations obeying a hard-core constraint. Such models can be systematically derived by renormalization schemes such as continuous unitary transformations or by variational approaches. Even in the absence of further interactions the hard-core constraint makes the dynamics of the hard-core bosons nontrivial. Here we develop a systematic diagrammatic approach to the spectral properties of hard-core bosons at finite temperature. Starting from an expansion in the density of thermally excited bosons in a system with an energy gap, our approach leads to a summation of ladder diagrams. Conceptually, the approach is not restricted to one dimension, but the one-dimensional case offers the opportunity to gauge the method by comparison to exact results obtained via a mapping to Jordan-Wigner fermions. In particular, we present results for the thermal broadening of single-particle spectral functions at finite temperature. The line-shape is found to be asymmetric at elevated temperatures and the band-width of the dispersion narrows with increasing temperature. Additionally, the total number of thermally excited bosons is calculated and compared to various approximations and analytic results. Thereby, a flexible approach is introduced which can also be applied to more sophisticated and higher dimensional models.

19 pages, 22 figures

References in corpus (7)

• Many-Body Physics with Ultracold Gases
• Finite-temperature lineshapes in gapped quantum spin chains
• Elementary excitations in gapped quantum spin systems
• Low-Temperature Dynamical Structure Factor of the Two-Leg Spin-1/2 Heisenberg Ladder
• Finite Temperature Dynamics of the Spin 1/2 Bond Alternating Heisenberg Antiferromagnetic Chain
• Quantum dynamics of an Ising spin-chain in a random transverse field
• Vertex corrections in the dynamic structure factor in spin ladders

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• Hard-core boson approach to the spin-1/2 triangular-lattice antiferromagnet Cs${}_2$CuCl${}_4$ at finite temperatures in magnetic fields higher than the saturation field
• Finite temperature dynamical correlations for the dimerized spin-1/2 chain
• Low temperature thermodynamics of multi-flavored hardcore bosons by the Brückner approach
• Time-dependent correlations in quantum magnets at finite temperature
• Low-energy spin excitations in field-induced phases of the spin-ladder antiferromagnet BiCu${}_2$PO${}_6$
• Evidence for strong correlations at finite temperatures in the dimerized magnet Na${}_2$Cu${}_2$TeO${}_6$
• Thermodynamics and renormalized quasi-particles in the vicinity of the dilute Bose gas quantum critical point in two dimensions
• Effects of Interactions on Dynamic Correlations of Hard-Core Bosons at Finite Temperatures