Velocity of excitations in ordered, disordered, and critical antiferromagnets

Sen, Arnab; Suwa, Hidemaro; Sandvik, Anders W.

doi:10.1103/physrevb.92.195145

Cited by 38 publications

(71 citation statements)

References 67 publications

(149 reference statements)

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“…We anticipate the most pronounced finite-size corrections to appear right at the quantum critical point: based on the relativistic invariance with a dynamical critical exponent z = 1, at low energies finite-size corrections of the peak position proportional to 1/L dominate at criticality. Indeed, enhanced finite-size corrections at the quantum critical point were reported recently for the low-energy dispersion of the Goldstone mode 44 , and are visible in Fig. 1 for g = 2.522, where a small finite-size gap at k = Q can be clearly resolved.…”

Section: A Quantum Monte Carlo Resultssupporting

confidence: 66%

Dynamical structure factors and excitation modes of the bilayer Heisenberg model

et al. 2015

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Using quantum Monte Carlo simulations along with higher-order spin-wave theory, bond-operator and strong-coupling expansions, we analyse the dynamical spin structure factor of the spin-half Heisenberg model on the square-lattice bilayer. We identify distinct contributions from the lowenergy Goldstone modes in the magnetically ordered phase and the gapped triplon modes in the quantum disordered phase. In the antisymmetric (with respect to layer inversion) channel, the dynamical spin structure factor exhibits a continuous evolution of spectral features across the quantum phase transition, connecting the two types of modes. Instead, in the symmetric channel we find a depletion of the spectral weight when moving from the ordered to the disordered phase. While the dynamical spin structure factor does not exhibit a well-defined distinct contribution from the amplitude (or Higgs) mode in the ordered phase, we identify an only marginally-damped amplitude mode in the dynamical singlet structure factor, obtained from interlayer bond correlations, in the vicinity of the quantum critical point. These findings provide quantitative information in direct relation to possible neutron or light scattering experiments in a fundamental two-dimensional quantum-critical spin system.

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Section: A Quantum Monte Carlo Resultssupporting

confidence: 66%

Dynamical structure factors and excitation modes of the bilayer Heisenberg model

et al. 2015

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“…The lowest singlet energy in the J-Q model at q c scales as 1/L, 52 as expected for a critical point with dynamic exponent z = 1. Thus, the critical domain wall energy is only slightly above the lowest singlet (and it should be noted here again that the momentum of all the states we are computing here is 0, as in the gound state).…”

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confidence: 67%

Emergent topological excitations in a two-dimensional quantum spin system

2015

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We study the mechanism of decay of a topological (winding-number) excitation due to finitesize effects in a two-dimensional valence-bond solid state, realized in an S = 1/2 spin model (J-Q model) with six-spin interactions and studied using projector Monte Carlo simulations in the valence bond basis. A topological excitation with winding number |W | > 0 contains domain walls, which are unstable due to the emergence of long valence bonds in the wave function, unlike in effective descriptions with the quantum dimer model (which by construction includes only short bonds). We find that the life time of the winding number in imaginary time, which is directly accessible in the simulations, diverges as a power of the system length L. The energy can be computed within this time (i.e., it converges toward a "quasi-eigenvalue" before the winding number decays) and agrees for large L with the domain-wall energy computed in an open lattice with boundary modifications enforcing a domain wall. Constructing a simplified two-state model which can be solved in real and imaginary time, and using the imaginary-time behavior from the simulations as input, we find that the real-time decay rate out of the initial winding sector is exponentially small in L. Thus, the winding number rapidly becomes a well-defined conserved quantum number for large systems, supporting the conclusions reached by computing the energy quasi-eigenvalues. Including Heisenberg exchange interactions which brings the system to a quantum-critical point separating the valencebond solid from an antiferromagnetic ground state (the putative "deconfined" quantum-critical point), we can also converge the domain wall energy here and find that it decays as a power-law of the system size. Thus, the winding number is an emergent quantum number also at the critical point, with all winding number sectors becoming degenerate in the thermodynamic limit. This supports the description of the critical point in terms of a U(1) gauge-field theory.

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“…Gap information can also be extracted by a direct analysis of the large-τ decay of the correlation functions [42,43]. Considering the spin sector, the smallest singlet-triplet gap occurs at q = Q and in the QD phase S(Q, τ ) is dominated by the triplon mode.…”

Section: Fig 1 Schematic Representation Of Ground States Excitationmentioning

confidence: 99%

“…In practice, these conditions can be hard to fulfil rigorously and it becomes necessary to go beyond the single-mode form by performing a fit to more than one exponential, or to perform a still more sophisticated analysis of the long-time decay of the correlation functions. Some methods for this task have been discussed recently [42,43]. Figure S1 shows two examples of spin correlation functions from the double-cubic Heisenberg model.…”

Section: Sii Stochastic Analytic Continuationmentioning

confidence: 99%

Amplitude Mode in Three-Dimensional Dimerized Antiferromagnets

et al. 2017

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The amplitude ("Higgs") mode is a ubiquitous collective excitation related to spontaneous breaking of a continuous symmetry. We combine quantum Monte Carlo (QMC) simulations with stochastic analytic continuation to investigate the dynamics of the amplitude mode in a three-dimensional dimerized quantum spin system. We characterize this mode by calculating the spin and dimer spectral functions on both sides of the quantum critical point, finding that both the energies and the intrinsic widths of the excitations satisfy field-theoretical scaling predictions. While the line width of the spin response is close to that observed in neutron scattering experiments on TlCuCl3, the dimer response is significantly broader. Our results demonstrate that highly non-trivial dynamical properties are accessible by modern QMC and analytic continuation methods.The spontaneous breaking of a continuous symmetry allows collective excitations of the direction and amplitude of the order parameter; for O(N ) symmetry, there are N−1 massless directional (Goldstone) modes and one massive amplitude mode [1][2][3][4]. In loose analogy with the Standard Model, the latter is often called a Higgs mode. A strongly damped amplitude mode has been reported in two dimensions (2D) at the Mott transition of ultracold bosons [5] and at the disorder-driven superconductorinsulator transition [6,7]. In 3D, the amplitude mode is expected on theoretical grounds to be more robust, and indeed the cleanest observation to date of a "Higgs boson" in condensed matter is at the pressure-induced magnetic quantum phase transition (QPT) in the dimerized quantum antiferromagnet TlCuCl 3 [8][9][10].Below the upper critical number of space-time dimensions, which for an O(N ) model is D c = 4, the amplitude mode is unstable, decaying primarily into pairs of Goldstone bosons [11][12][13]. In both 2D and 3D, the longitudinal dynamic susceptibility exhibits an infrared singularity due to the Goldstone modes [14], whose consequences for the visibility of the amplitude mode have been investigated extensively in 2D [15][16][17]. It was noted [14] that the scalar O(N )-symmetric susceptibility remains uncontaminated by infrared contributions, which should permit the amplitude mode to be observed as a welldefined peak. The (3+1)D O(3) case of TlCuCl 3 is at D c and the amplitude mode is critically damped, meaning that its width is proportional to its energy at the meanfield level [9,[18][19][20]. This mode can be probed through the spin response (longitudinal susceptibility) by neutron spectroscopy, and measurements over a wide range of pressures reveal a rather narrow peak width of just 15% of the excitation energy [10]. The value of this nearconstant width-to-energy ratio is the key to the mode visibility, thus calling for unbiased numerical calculations in suitable model Hamiltonians.FIG. 1. Schematic representation of ground states, excitation processes, and corresponding gaps in a dimerized antiferromagnet. The ratio g = J /J of the intra-and inter-dimer coupling constants ...

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Velocity of excitations in ordered, disordered, and critical antiferromagnets

Cited by 38 publications

References 67 publications

Dynamical structure factors and excitation modes of the bilayer Heisenberg model

Dynamical structure factors and excitation modes of the bilayer Heisenberg model

Emergent topological excitations in a two-dimensional quantum spin system

Amplitude Mode in Three-Dimensional Dimerized Antiferromagnets

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