During my PhD (Boston University, 2001-2006), my research under the supervision of Prof. Claudio Chamon focused on understanding the physics of classical and quantum constrained systems without disorder. At the classical level, these systems are shown to exhibit a broad range of complex behaviors, from exotic thermodynamic phases and phase transitions, to dynamical obstruction of equilibration and glassiness.
In collaboration with Prof. Pierre Pujol, we investigated some detailed case studies of constrained systems such as dimer and coloring models [1]. In particular, we showed how the polymorphic nature of these models requires the use of diverse analytical (conformal field theory, cluster variational mean field) and numerical (Monte Carlo, transfer matrix) techniques in order to gain a thorough understanding of their behavior.
We then shifted our attention towards understanding the role played by strong constraints in quantum Hamiltonians. Compared to their classical counterparts, the analysis of these quantum systems is more challenging and a detailed insight cannot be achieved in general. In collaboration with Prof. Pierre Pujol and with Prof. Christopher Mudry, we showed how quantum hard constrained systems can exhibit a high-temperature universal scaling regime, as identified by the power law decay of some spatial correlation functions [2]. This is particularly intriguing as it suggests a possible alternative interpretation for the quantum critical regime experimentally observed in strongly correlated systems. Moreover, the interplay of hard constraints and topological order is shown to give rise to relaxation times that are exponential in system size -- a signature of quantum glassiness [3]. These systems are indeed ideal candidates to study the origins of quantum glassiness in the absence of disorder.
Finally, we proposed a new technique that establishes in a constructive way a one-to-one correspondence between stochastic (Markovian) classical systems and a specific class of quantum Hamiltonian representations, dubbed Stochastic Matrix Form (SMF) decompositions [4]. The SMF technique can be used to investigate existing quantum Hamiltonians when their known representations fall into this special class. Conversely, one can use it to construct new quantum Hamiltonians given a stochastic classical system. This turns out to be particularly convenient for example to study quantum systems in the presence of hard constraints, at least in the case of specially fine-tuned Hamiltonians, as we illustrated with a few examples on some novel dimer models [5].
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C. Castelnovo, P. Pujol, and C. Chamon
Dynamical obstruction in a constrained system and its realization in lattices of superconducting devices
Physical Review B 69, 104529 (2004) -
C. Castelnovo, C. Chamon, C. Mudry and P. Pujol
High-Temperature Criticality in Strongly Constrained Quantum Systems
Physical Review B 73, 144411 (2006) -
C. Castelnovo, C. Chamon, C. Mudry and P. Pujol
Quantum three-coloring dimer model and the disruptive effect of quantum glassiness on its line of critical points
Physical Review B 72, 104405 (2005) -
C. Castelnovo, C. Chamon, C. Mudry and P. Pujol
From quantum mechanics to classical statistical physics: Generalized Rokhsar-Kivelson Hamiltonians and the ``Stochastic Matrix Form'' decomposition
Annals of Physics 318, 316 (2005) -
C. Castelnovo, C. Chamon, C. Mudry and P. Pujol
Zero-temperature Kosterlitz-Thouless transition in a two-dimensional quantum system
Annals of Physics 322, 903 (2007)