Studies of strongly disordered quantum systems

Author(s)

Victor Luiz Quito

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Física Gleb Wataghin
• Defense date: 2016-02-22

Examining board members

Eduardo Miranda; Alex Antonelli; Ricardo Luís Doretto; André de Pinho Vieira; Francisco Castilho Alcaraz

• Advisor: Eduardo Miranda

Abstract

One-dimensional random systems are known to present phenomena that have no analog in the zero-disorder limit or in higher dimensions. Among the phenomena inherent to disordered systems are the antiferromagnetic phases of spin systems, where the ground state is formed by a collection of spin pairs, and the Anderson localization, where disorder leads to the exponential decay of the wave function. In this Thesis, we study some cases where the low-energy physics is dramatically changed by disorder, including the two previous examples mentioned above. Besides systems that provide the physical properties listed above, we elucidate a generic mechanism that allows the symmetry enhancement in random spin systems, a theme that was previously unexplored. We investigate the effects of disorder in generic one-dimensional spin chains, with spins coupled by interactions that are invariant under rotation of the system's coordinates and time reversal. We consider all the possible terms that respect those symmetries. These terms go beyond the standard Heisenberg couplings in chains where S>1/2. In spin-1 chains, we find distinct antiferromagnetic phases, where the ground state is formed by a collection of spin singlets, whose positions are arbitrary. In low energies, the effective disorder in such phases grow without bounds, and, therefore, these phases are called "infinite-disorder phases". Even more surprising is the fact that in these antiferromagnetic phases, the low-energy symmetry is enhanced, from SU(2) to SU(3). In order to make such claim, we map out the spin operators, including monopolar, dipolar and quadrupolar operators, into generators of SU(3) representations. We verify that the low energy physics is invariant under rotation that use this set of operators as generators. In analogy with particle physics, one of the phases is a "baryonic phase", where the ground state is a collection of three-spin singlets (or quarks that are bounded to form color singlets, using the high-energy analogy), while the other phase is of the "mesonic" type, with the ground state formed by spin pairs (or quark-antiquark pairs, using the analogy). Besides the antiferromagnetic phases, we map the complete phase diagram of the spin-1 bilinear and biquadratic spin chains in the finite disorder regime, including also the ferromagnetic phase and a large spin phase. In the latter, the ferromagnetism and antiferromagnetism compete. This competition reflects on the effective spin size. These effective spins are the low-energy degrees of freedom, and the growth is slower than in the ferromagnetic case. Unlike in the antiferromagnetic phase, in these other phases, the effective disorder saturates at a finite value. We extend the study to spins greater than one by using irreducible spherical tensors, that are shown to be the natural language for building the decimations and the the strong-disorder renormalization group flow. Again, we include all the possible terms that are invariant under SU(2) rotations and time reversal. We find that the low energy physics of antiferromagnetic phases present a symmetry enhancement, with the SU(2S+1) being the low-energy symmetry. This symmetry is inherited from a point in the parameter space where the mapping to SU(2S+1) is exact in all energy scales. This is a generalization of the "mesonic" SU(3) phase. We also discuss why the "baryonic" phases are much more restrictive, and present only in the spin-1 chain. Another system that we consider is the non-interacting long-range hopping fermionic chain. The hoppings are chosen with a standard deviation decaying as a power-law with distance. To study such chains, we extend the Flow Equation Method, developed by Wegner, for systems with disorder. Coupled to this extension of the method, we develop a renormalization group technique, which allowed us to map the full phase diagram, with an extended phase at decaying exponents less than one, and a localized phase for exponents greater than one. The localized or delocalized phases can be probed by either the evolution of the coupling distribution or by the eigenvalues of the Hamiltonian, and its associated level repulsion (AU)

• FAPESP's process: 09/17531-3 - Studies of strongly disordered quantum systems
• Grantee: Victor Luiz Quito
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)