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arXiv:0905.0693 · Condensed Matter Physics

Revealing novel quantum phases in quantum antiferromagnets on random lattices

Yu, Stephan Haas, Roscilde

Published Jan 1, 2009• 0 citations
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Abstract

Quantum magnets represent an ideal playground for the controlled realization of novel quantum phases and of quantum phase transitions.The Hamiltonian of the system can be indeed manipulated by applying a magnetic field or pressure on the sample.When doping the system with non-magnetic impurities, novel inhomogeneous phases emerge from the interplay between geometric randomness and quantum fluctuations.In this paper we review our recent work on quantum phase transitions and novel quantum phases realized in disordered quantum magnets.The system inhomogeneity is found to strongly affect phase transitions by changing their universality class, giving the transition a novel, quantum percolative nature.Such transitions connect conventionally ordered phases to unconventional, quantum disordered ones -quantum Griffiths phases, magnetic Bose glass phases -exhibiting gapless spectra associated with low-energy localized excitations.

DOI
10.5488/cmp.12.3.519

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Quantum magnets represent an ideal playground for the controlled realization of novel quantum phases and of quantum phase transitions.The Hamiltonian of the system can be indeed manipulated by applying a magnetic field or pressure on the sample.When doping the system with non-magnetic impurities, novel inhomogeneous phases emerge from the interplay between geometric randomness and quantum fluctuations.In this paper we review our recent work on quantum phase transitions and novel quantum phases realized in disordered quantum magnets.The system inhomogeneity is found to strongly affect phase transitions by changing their universality class, giving the transition a novel, quantum percolative nature.Such transitions connect conventionally ordered phases to unconventional, quantum disordered ones -quantum Griffiths phases, magnetic Bose glass phases -exhibiting gapless spectra associated with low-energy localized excitations.
The interplay of geometric randomness and strong quantum fluctuations is an exciting topic in quantum many-body physics, leading to the emergence of novel quantum phases in strongly correlated electron systems. Recent investigations have focused on the case of homogeneous site and bond dilution in the quantum antiferromagnet on the square lattice, reporting a classical geometric percolation transition between magnetic order and disorder. In this study we show how inhomogeneous bond dilution leads to percolative quantum phase transitions, which we have studied extensively by quantum Monte Carlo simulations. Quantum percolation introduces a new class of two-dimensional spin liquids, characterized by an infinite percolating network with vanishing antiferromagnetic order parameter.
We report on the non‐trivial interplay between geometric randomess and quantum fluctuations in two‐dimensional S = 1/2 Heisenberg antiferromagnets (AFs), studied by quantum Monte Carlo. The case of the inhomogeneously bond‐diluted square lattice AF in zero field and of the site‐diluted bilayer AF in a finite magnetic field are emblematic examples of randomness‐induced quantum‐disordered phases on percolated lattices. These phases display unconventional properties, being gapless but with a finite correlation length.
A quantum particle cannot in general diffuse through a disordered medium because of its wavelike nature, but interacting particles can escape localization by collectively percolating through the system. For bosonic particles this phenomenon corresponds to a quantum transition from a localized insulator phase —the Bose glass— to a superfluid phase, in which particles condense into an extended state. Here, we construct a universal phase diagram of disordered bosons in doped quantum magnets for which bosonic quasiparticles are represented by magnetized states (spin triplets) of the quantum spins, condensing into a magnetically ordered state. The appearance of a Bose glass leads to strong measurable signatures in the onset of superfluidity of the spin-triplet gas, exhibiting a complex crossover from low-temperature quantum percolation to a conventional condensation transition at intermediate temperatures.
We investigate quantum phase transitions in the spin-1∕21∕21∕2 Heisenberg antiferromagnet on square lattices with inhomogeneous bond dilution. It is shown that quantum fluctuations can be continuously tuned by inhomogeneous bond dilution, eventually leading to the destruction of long-range magnetic order on the percolating cluster. Two multicritical points are identified at which the magnetic transition separates from the percolation transition, introducing a quantum phase transition. Beyond these multicritical points a quantum-disordered phase appears, characterized by an infinite percolating cluster with short ranged antiferromagnetic order. In this phase, the low-temperature uniform susceptibility diverges algebraically with non-universal exponents. This is a signature that the quantum-disordered phase is a quantum Griffiths phase, as also directly confirmed by the statistical distribution of local gaps. This study thus presents evidence of a genuine quantum Griffiths phenomenon in a two-dimensional Heisenberg antiferromagnet.
Impurities, defects, and other types of imperfections are ubiquitous in realistic quantum many-body systems and essentially unavoidable in solid state materials. Often, such random disorder is viewed purely negatively as it is believed to prevent interesting new quantum states of matter from forming and to smear out sharp features associated with the phase transitions between them. However, disorder is also responsible for a variety of interesting novel phenomena that do not have clean counterparts. These include Anderson localization of single-particle wave functions, many-body localization in isolated many-body systems, exotic quantum critical points, and glassy ground-state phases. This brief review focuses on two separate but related subtopics in this field. First, we review under what conditions different types of randomness affect the stability of symmetry-broken low-temperature phases in quantum many-body systems and the stability of the corresponding phase transitions. Second, we discuss the fate of quantum phase transitions that are destabilized by disorder as well as the unconventional quantum Griffiths phases that emerge in their vicinity.
We show that the interplay of geometric criticality and quantum fluctuations leads to a novel universality class for the percolation quantum phase transition in diluted magnets. All critical exponents involving dynamical correlations are different from the classical percolation values, but in two dimensions they can nonetheless be determined exactly. We develop a complete scaling theory of this transition, and we relate it to recent experiments in La2Cu(1-p)(Zn,Mg)(p)O4. Our results are also relevant for disordered interacting boson systems.