Deconfined quantum critical points -I

2012

We show that the concept of bipartite fluctuations F provides a very efficient tool to detect quantum phase transitions in strongly correlated systems. Using state of the art numerical techniques complemented with analytical arguments, we investigate paradigmatic examples for both quantum spins and bosons. As compared to the von Neumann entanglement entropy, we observe that F allows to find quantum critical points with a much better accuracy in one dimension. We further demonstrate that F can be successfully applied to the detection of quantum criticality in higher dimensions with no prior knowledge of the universality class of the transition. Promising approaches to experimentally access fluctuations are discussed for quantum antiferromagnets and cold gases.

Physical Review B, 2011

In certain Mott-insulating dimerized antiferromagnets, triplet excitations of the paramagnetic phase can decay into the two-particle continuum. When such a magnet undergoes a quantum phase transition into a magnetically ordered state, this coupling becomes part of the critical theory provided that the lattice ordering wavevector is zero. One microscopic example is the staggered-dimer antiferromagnet on the square lattice, for which deviations from O(3) universality have been reported in numerical studies. Using both symmetry arguments and microscopic calculations, we show that a non-trivial cubic term arises in the relevant order-parameter quantum field theory, and assess its consequences using a combination of analytical and numerical methods. We also present finite-temperature quantum Monte Carlo data for the staggered-dimer antiferromagnet which complement recently published results. The data can be consistently interpreted in terms of critical exponents identical to that of the standard O(3) universality class, but with anomalously large corrections to scaling. We argue that the two-particle decay of critical triplons, although irrelevant in two spatial dimensions, is responsible for the leading corrections to scaling due to its small scaling dimension.

Citation for published version (APA): Bishop, RF., Xian, Y., & Zeng, C. (1996). A coherent microscopic approach to quantum criticality: Applications to antiferromagnets on square and triangular lattices. In E. V. Ludeña, P. Vashishta, & R. F. Bishop (Eds.), Condensed Matter Theories (Vol. 11, pp. 91-102). Nova Science Publishers. http://personalpages.manchester.ac.uk/staff/raymond.bishop/RFB_papers/[131] CMT_11(1996)91

Physical Review B, 2004

The nearest-neighbor quantum-antiferromagnetic (AF) Heisenberg model for spin 1/2 on a twodimensional square lattice is studied in the auxiliary-fermion representation. Expressing spin operators by canonical fermionic particles requires a constraint on the fermion charge Qi = 1 on each lattice site i , which is imposed approximately through the thermal average. The resulting interacting fermion system is first treated in mean-field theory (MFT), which yields an AF ordered ground state and spin waves in quantitative agreement with conventional spin-wave theory. At finite temperature a self-consistent approximation beyond mean field is required in order to fulfill the Mermin-Wagner theorem. We first discuss a fully self-consistent approximation, where fermions are renormalized due to fluctuations of their spin density, in close analogy to FLEX. While static properties like the correlation length, ξ(T ) ∝ exp(a J/T ) , come out correctly, the dynamical response lacks the magnon-like peaks which would reflect the appearance of short-range order at low T . This drawback, which is caused by overdamping, is overcome in a 'minimal self-consistent approximation' (MSCA), which we derive from the equations of motion. The MSCA features dynamical scaling at small energy and temperature and is qualitatively correct both in the regime of order-parameter relaxation at long wavelengths λ > ξ and in the short-range-order regime at λ < ξ . We also discuss the impact of vertex corrections and the problem of pseudo-gap formation in the single-particle density of states due to long-range fluctuations. Finally we show that the (short-range) magnetic order in MFT and MSCA helps to fulfill the constraint on the local fermion occupancy.

Physical Review Letters, 2012

By means of nuclear spin-lattice relaxation rate T −1 1 , we follow the spin dynamics as a function of the applied magnetic field in two gapped one-dimensional quantum antiferromagnets: the anisotropic spin-chain system NiCl2-4SC(NH2)2 and the spin-ladder system (C5H12N)2CuBr4. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapples Tomonaga-Luttinger-liquid state. In between, T −1 1 exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for T −1 1 , compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum critical behavior.

1999

The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately. arXiv:cond-mat/9812341v1 [cond-mat.stat-mech] Transfer-matrix scaling methods have been used to study critical properties of field-induced phase transitions of two distinct two-dimensional antiferromagnets with discrete-symmetry order parameters: triangular-lattice Ising systems (TIAF) and the square-lattice three-state Potts model (SPAF-3). Our main findings are summarised as follows. For TIAF, we have shown that the critical line leaves the zero-temperature, zero-field fixed point at a finite angle. Our best estimate of the slope at the origin is (dTc/dH) T =H=0 = 4.74 ± 0.15. For SPAF-3 we provided evidence that the zero-field correlation length diverges as ξ(T → 0, H = 0) ≃ exp(a/T x ), with x = 1.08 ± 0.13, through analysis of the critical curve at H = 0 plus crossover arguments. For SPAF-3 we have also ascertained that the conformal anomaly and decay-of-correlations exponent behave as: (a) H = 0: c = 1, η = 1/3; (b) H = 0: c = 1/2, η = 1/4.

Science, 2000

Published in Science 288, 475 (2000).

Nature Physics, 2019

Strange-metal phenomena often develop at the border of antiferromagnetic order in strongly correlated metals. It has been well established that they can originate from the fluctuations anchored by the point of continuous quantum phase transition out of the antiferromagnetic order, i.e., a quantum critical point. What has been unclear is how these phenomena can be associated with a potential new phase of matter at zero temperature. Here we show that magnetic frustration of the 4f-local moments in the distorted Kagome intermetallic compound CePdAl gives rise to such a paramagnetic quantum-critical phase. Moreover, we demonstrate that this phase turns into a Fermi liquid through a Mott-like crossover; in a two-dimensional parameter space of pressure and magnetic field, this crossover is linked to a line of zero-temperature 4f-electron localization-delocalization phase transitions at low and moderate pressures. Our discovery motivates a new design principle for strongly correlated metallic states with unconventional excitations that may underlie the development of such effects as high temperature superconductivity. Geometrical frustration in quantum-spin systems gives rise to quantum fluctuations which may suppress long-range magnetic order and cause a quantum-spin-liquid ground state [1]. This notion is traditionally associated with insulating magnets only. There has been increasing recognition, however, that geometrical frustration is also important to bad metals that host local moments, such as strongly correlated f-electron metals [2-7], which provide a prototype setting

Physical Review Letters, 2018

We study the Néel-paramagnetic quantum phase transition in two-dimensional dimerized S = 1/2 Heisenberg antiferromagnets using finite-size scaling of quantum Monte Carlo data. We resolve the long standing issue of the role of cubic interactions arising in the bond-operator representation when the dimer pattern lacks a certain symmetry. We find non-monotonic (monotonic) size dependence in the staggered (columnar) dimerized model, where cubic interactions are (are not) present. We conclude that there is a new irrelevant field in the staggered model, but, at variance with previous claims, it is not the leading irrelevant field. The new exponent is ω2 ≈ 1.25 and the prefactor of the correction L −ω 2 is large and comes with a different sign from that of the conventional correction with ω1 ≈ 0.78. Our study highlights competing scaling corrections at quantum critical points.

Physical Review B

Heavy fermion systems, and other strongly correlated electron materials, often exhibit a competition between antiferromagnetic (AF) and singlet ground states. Using exact Quantum Monte Carlo (QMC) simulations, we examine the effect of impurities in the vicinity of such AFsinglet quantum critical point (QCP), through an appropriately defined "impurity susceptibility," χimp. Our key finding is a connection, within a single calculational framework, between AF domains induced on the singlet side of the transition, and the behavior of the nuclear magnetic resonance (NMR) relaxation rate 1/T1. We show that local NMR measurements provide a diagnostic for the location of the QCP which agrees remarkably well with the vanishing of the AF order parameter and large values of χimp.

Science, 2020

Strange metal behavior is ubiquitous in correlated materials, ranging from cuprate superconductors to bilayer graphene, and may arise from physics beyond the quantum fluctuations of a Landau order parameter. In quantum-critical heavy-fermion antiferromagnets, such physics may be realized as critical Kondo entanglement of spin and charge and probed with optical conductivity. We present terahertz time-domain transmission spectroscopy on molecular beam epitaxy–grown thin films of YbRh2Si2, a model strange-metal compound. We observed frequency over temperature scaling of the optical conductivity as a hallmark of beyond-Landau quantum criticality. Our discovery suggests that critical charge fluctuations play a central role in the strange metal behavior, elucidating one of the long-standing mysteries of correlated quantum matter.

Journal of Statistical Mechanics: Theory and Experiment, 2005

Antiferromagnetic Hamiltonians with short-range, non-frustrating interactions are well-known to exhibit long range magnetic order in dimensions, d ≥ 2 but exhibit only quasi long range order, with power law decay of correlations, in d = 1 (for half-integer spin). On the other hand, non-frustrating long range interactions can induce long range order in d = 1. We study Hamiltonians in which the long range interactions have an adjustable amplitude λ, as well as an adjustable power-law 1/|x| α , using a combination of quantum Monte Carlo and analytic methods: spin-wave, large-N non-linear σ model, and renormalization group methods. We map out the phase diagram in the λ-α plane and study the nature of the critical line separating the phases with long range and quasi long range order. We find that this corresponds to a novel line of critical points with continuously varying critical exponents and a dynamical exponent, z < 1.

Physical Review B, 2010

We investigate the stability of Quantum Critical Points (QCPs) in the presence of two competing phases. These phases near QCPs are assumed to be either classical or quantum and assumed to repulsively interact via square-square interactions. We find that for any dynamical exponents and for any dimensionality strong enough interaction renders QCPs unstable, and drives transitions to become first order. We propose that this instability and the onset of first-order transitions lead to spatially inhomogeneous states in practical materials near putative QCPs. Our analysis also leads us to suggest that there is a breakdown of Conformal Field Theory (CFT) scaling in the Anti de Sitter models, and in fact these models contain first-order transitions in the strong coupling limit.

Physical Review B, 2010

The spin texture surrounding a non-magnetic impurity in a quantum antiferromagnet is a sensitive probe of the novel physics of a class of quantum phase transitions between a Neel ordered phase and a valence bond solid phase in square lattice S=1/2 antiferromagnets. Using a newly developed T=0 Quantum Monte Carlo technique, we compute this spin texture at these transitions and find that it does not obey the universal scaling form expected at a scale invariant quantum critical point. We also identify the precise logarithmic form of these scaling violations. Our results are expected to yield important clues regarding the probable theory of these unconventional transitions.

Physical Review B, 2000

We present a study of the critical phenomena around the quantum critical point in heavy-fermion systems. In the framework of the S = 1/2 Kondo lattice model, we introduce an extended decoupling scheme of the Kondo interaction which allows one to treat the spin fluctuations and the Kondo effect on an equal footing. The calculations, developed in a self-consistent oneloop approximation, lead to the formation of a damped collective mode with a dynamic exponent z = 2 in the case of an antiferromagnetic instability. The system displays a quantum-classical crossover at finite temperature depending how the energy of the mode, on the scale of the magnetic correlation length, compares to k B T. The low temperature behavior, in the different regimes separated by the crossover temperatures, is then discussed for both 2-and 3-dimensional systems.