Quantum criticality: beyond the Landau-Ginzburg-Wilson paradigm

Physical Review B, 2007

We perform a renormalization group analysis of some important effective field theoretic models for deconfined spinons. We show that deconfined spinons are critical for an isotropic SU(N) Heisenberg antiferromagnet, if N is large enough. We argue that nonperturbatively this result should persist down to N = 2 and provide further evidence for the so called deconfined quantum criticality scenario. Deconfined spinons are also shown to be critical for the case describing a transition between quantum spin nematic and dimerized phases. On the other hand, the deconfined quantum criticality scenario is shown to fail for a class of easy-plane models. For the cases where deconfined quantum criticality occurs, we calculate the critical exponent η for the decay of the two-spin correlation function to first-order in ǫ = 4 − d. We also note the scaling relation η = d + 2(1 − ϕ/ν) connecting the exponent η for the decay to the correlation length exponent ν and the crossover exponent ϕ. PACS numbers: 75.30.Kz,64.60.Cn,71.30.+h,

Physical Review B, 2011

The ground-state (GS) phase diagram of the frustrated spins J1-J2-J3 Heisenberg antiferromagnet on the honeycomb lattice is studied using the coupled cluster method implemented to high orders of approximation, for spin quantum numbers s = 1, 3 2 , 2 , 5 2. The model has antiferromagnetic (AFM) nearest-neighbour, next-nearest-neighbour and next-nextnearest-neighbour exchange couplings (with strength J1 > 0, J2 > 0 and J3 > 0, respectively). We specifically study the case J3 = J2 = κJ1, in the range 0 ≤ κ ≤ 1 of the frustration parameter, which includes the point of maximum classical (s → ∞) frustration, viz., the classical critical point at κ cl = 1 2 , which separates the Néel phase for κ < κ cl and the collinear striped AFM phase for κ > κ cl. Results are presented for the GS energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. For all spins s ≥ 3 2 we find a quantum phase diagram very similar to the classical one, with a direct first-order transition between the two collinear AFM states at a value κc(s) which is slightly greater than κ cl [e.g., κc(3 2) ≈ 0.53(1)] and which approaches it monotonically as s → ∞. By contrast, for the case s = 1 the transition is split into two such that the stable GS phases are one with Néel AFM order for κ < κc 1 = 0.485(5) and one with striped AFM order for κ > κc 2 = 0.528(5), just as in the case s = 1 2 (for which κc 1 ≈ 0.47 and κc 2 ≈ 0.60). For both the s = 1 2 and s = 1 models the transition at κc 2 appears to be of first-order type, while that at κc 1 appears to be continuous. However, whereas in the s = 1 2 case the intermediate phase appears to have PVBC order over the entire range κc 1 < κ < κc 2 , in the s = 1 case PVBC ordering either exists only over a very small part of the region or, more likely, is absent everywhere.

Europhysics Letters (EPL), 2006

Recently it was argued that quantum phase transitions can be radically different from classical phase transitions with as a highlight the 'deconfined critical points' exhibiting fractionalization of quantum numbers due to Berry phase effects. Such transitions are supposed to occur in frustrated ('J1-J2') quantum magnets. We have developed a novel renormalization approach for such systems which is fully respecting the underlying lattice structure. According to our findings, another profound phenomenon is around the corner: a fluctuation induced (order-out-of-disorder) first order transition. This has to occur for large spin and we conjecture that it is responsible for the weakly first order behavior recently observed in numerical simulations for frustrated S = 1/2 systems.

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, 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.

Communications Physics

In quantum many-body systems with local interactions, the effects of boundary conditions are considered to be negligible, at least for sufficiently large systems. Here we show an example of the opposite. We consider a spin chain with two competing interactions, set on a ring with an odd number of sites. When only the dominant interaction is antiferromagnetic, and thus induces topological frustration, the standard antiferromagnetic order (expressed by the magnetization) is destroyed. When also the second interaction turns from ferro to antiferro, an antiferromagnetic order characterized by a site-dependent magnetization which varies in space with an incommensurate pattern, emerges. This modulation results from a ground state degeneracy, which allows to break the translational invariance. The transition between the two cases is signaled by a discontinuity in the first derivative of the ground state energy and represents a quantum phase transition induced by a special choice of boundar...

2003

Antiferromagnetic Heisenberg integer-spin chains are characterized by a spin-liquid ground state with no long-range order, due to the relevance of quantum fluctuations. Spin anisotropy, however, freezes quantum fluctuations, and the system is magnetized in the presence of a sufficiently large easy-axis anisotropy. We numerically investigate the case S = 1, by means of the density-matrix renormalization group, and find that the freezing of the spin liquid into a Néel spin solid, with increasing easy-axis anisotropy, is a continuous quantum phase transition. Numerical evidence indicates that the transition is not in the two-dimensional Ising universality class. PACS numbers: 75.10.Jm, 75.30.Cr, 75.40.Mg Quantum fluctuations play a crucial role in antiferromagnetic (AFM) Heisenberg spin chains, as they are strong enough to suppress magnetic long-range order at zero temperature. Despite the common absence of a spontaneous staggered magnetization in the ground state, the physical properties are, however, different for integer and half-integer spin S [1]. Indeed, half-integerspin chains are characterized by a gapless excitation spectrum, power-law spin-spin correlations, and a divergent linear response to a staggered magnetic field, and are therefore usually considered as nearly ordered. The spectrum of integer-spin chains is instead gapped in the thermodynamic limit, with a finite linear response to staggered magnetic fields. The ground state is a spin liquid with finite spin-spin correlation length, and the gap to the first excited state is usually called Haldane gap.

150 Years Of Quantum Many-Body Theory - A Festschrift in Honour of the 65th Birthdays of John W Clark, Alpo J Kallio, Manfred L Ristig and Sergio Rosati, 2001

We discuss the influence of strong quantum fluctuations on zero-temperature phase transitions in a two-dimensional spin-half Heisenberg system. Using a high-order coupled cluster treatment, we study competition of magnetic bonds with and without frustration. We find that the coupled cluster treatment is able to describe the zero-temperature transitions in a qualitatively correct way, even if frustration is present and other methods such as quantum Monte Carlo fail.

Journal of Physics: Condensed Matter, 2008

A recent study revealed the dynamics of the charge sector of a one-dimensional quarter-filled electronic system with extended Hubbard interactions to be that of an effective pseudospin transversefield Ising model (TFIM) in the strong coupling limit. With the twin motivations of studying the co-existing charge and spin order found in strongly correlated chain systems and the effects of inter-chain couplings, we investigate the phase diagram of coupled effective (TFIM) systems. A bosonisation and RG analysis for a two-leg TFIM ladder yields a rich phase diagram showing Wigner/Peierls charge order and Neel/dimer spin order. In a broad parameter regime, the orbital antiferromagnetic phase is found to be stable. An intermediate gapless phase of finite width is found to lie in between two charge-ordered gapped phases. Kosterlitz-Thouless transitions are found to lead from the gapless phase to either of the charge-ordered phases. A detailed analysis is also carried out for the dimensional crossover physics when many such pseudospin systems are coupled to one another. Importantly, the analysis reveals the key role of critical quantum fluctuations in driving the strong dispersion in the transverse directions, as well as a T = 0 deconfinement transition. Our work is potentially relevant for a unified description of a class of strongly correlated, quarter-filled chain and ladder systems.

Nuclear Physics B, 2007

It has been proposed that there are new degrees of freedom intrinsic to quantum critical points that contribute to quantum critical physics. We study 2+1 D antiferromagnets in order to explore possible new quantum critical physics arising from nontrivial topological effects. We show that skyrmion excitations are stable at criticality and have nonzero probability at arbitrarily low temperatures. To include quantum critical skyrmion effects, we find a class of exact solutions composed of skyrmion and antiskyrmion superpositions, which we call topolons. We include the topolons in the partition function and renormalize by integrating out small size topolons and short wavelength spin waves. We obtain a correlation length critical exponent ν = 0.9297 and anomalous dimension η = 0.3381.