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Emergent Phenomena in Quantum Critical Systems
A quantum critical point (QCP) is a point in the phase diagram of quantum matter where a continuous phase transition takes place at zero temperature. Low-dimensional quantum critical systems are strongly correlated, therefore hosting nontrivial emergent phenomena. In this thesis, we first address two decades-old problems on quantum critical dynamics. We then reveal two novel emergent phenomena of quantum critical impurity problems. In the first part of the thesis, we address the linear response dynamics of the -dimensional quantum critical universality class, which can be realized in the ultracold bosonic system near the superfluid (SF) to Mott insulator (MI) transition in two dimensions. The first problem we address is about the fate of the massive Goldstone (Higgs) mode in the two-dimensional relativistic theory. Using large-scale Monte Carlo simulations and numerical analytical continuation, we obtain universal spectral functions in SF, MI and normal quantum critical liquid phases and reveal that they all have a relatively sharp resonant peak before saturating to the critical plateau behavior at higher frequencies. The universal resonance peak in SF reveals a critically-defined massive Goldstone boson, while the peaks in the last two phases are beyond the predictions of previous theories. The second problem we address is to controllably calculate one of the most fundamental transport properties---optical conductivity---in the quantum critical region. We precisely determine the conductivity on the quantum critical plateau, with the conductivity quantum. For the first time, the shape of the function in the Matsubara representation is accurate enough to compare a holographic gauge-gravity duality theory for transport properties [Myers, Sachdev, and Singh, Phys. Rev. D 83, 066017 (2011)] to the reality. We find that the theory---in the original form---can not account for our data, thereby inspiring the theorists to modify the corresponding holographic theory. The second part of this thesis discusses two exotic impurity states hosted by quantum critical environments. The first one is the halon, a novel critical state of an impurity in quantum critical environment. We find that varying the impurity-environment interaction leads to a boundary quantum critical point (BQCP) between two competing ground states with charges differing by . In the vicinity of the BQCP, the halon phenomenon emerges. The hallmark of the halon physics is that a well-defined integer charge carried by the impurity gets fractionalized into two parts: a microscopic core with half-integer charge and a critically large halo carrying a complementary charge of . The halon can be generalized to other incompressible quantum-critical environments with particle-hole symmetry. The second novel phenomenon we reveal is termed trapping collapse . We address a simple fundamental question of how many repulsively interacting bosons can be localized by a trapping potential. We find that under rather generic conditions, for both weakly and strongly repulsive particles, in two and three dimensions---but not in one-dimension!---this potential well can trap infinitely many bosons. Even hard-core repulsive interactions do not prevent this effect from taking place. Our results imply that an attractive impurity in a generic SF-MI quantum critical environment can carry divergent charges
Topological Phase Transitions in Line-nodal Superconductors
Fathoming interplay between symmetry and topology of many-electron
wave-functions has deepened understanding of quantum many body systems,
especially after the discovery of topological insulators. Topology of electron
wave-functions enforces and protects emergent gapless excitations, and symmetry
is intrinsically tied to the topological protection in a certain class. Namely,
unless the symmetry is broken, the topological nature is intact. We show novel
interplay phenomena between symmetry and topology in topological phase
transitions associated with line-nodal superconductors. The interplay may
induce an exotic universality class in sharp contrast to that of the
phenomenological Landau-Ginzburg theory. Hyper-scaling violation and emergent
relativistic scaling are main characteristics, and the interplay even induces
unusually large quantum critical region. We propose characteristic experimental
signatures around the phase transitions in three spatial dimensions, for
example, a linear phase boundary in a temperature-tuning parameter
phase-diagram.Comment: 4 + 23 pages, 7 figures, 1 table; the first two authors contributed
equally to this wor
Quantum Monte Carlo studies of phase transitions
Phase transitions have been an active area of research in statistical mechanics for almost a century and have recently been integrated into quantum mechanics. Many phenomena such as superconductivity and unconventional magnetism are understood to arise from exotic quantum phases and at points describing quantum phase transitions. A detailed understanding of these phase transitions requires numerical simulations of models which benchmark realistic models against theoretical frameworks. The topic of this thesis is the implementation of Quantum Monte Carlo simulation, which is a powerful technique to understand quantum condensed matter, in interesting models to illustrate novel phenomena in magnetic systems. The novel features of condensed matter systems described in this thesis consist of emergent symmetries at critical points, interesting dynamical features of such systems and the drastic effects of defects in spin systems used in the field of adiabatic quantum computing. Emergent symmetries are shown by condensed matter systems especially at critical points and are features which cannot be shown by individual or a small number of spins. Examples of this in one and two dimensions are presented in an early chapter of this thesis. In addition to this, spin systems can show excitations which have an interesting spatial structure as a consequence of restricted dynamics which only allow the excitations to spread in a particular region. This is presented in the context of a simple model in the following chapter along with numerical support. The following chapter contains a description of adiabatic quantum computing along with a particular model which we study. The phase transition and the effects on the performance of adiabatic quantum computing are studied in this context
An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
Continuous quantum phase transitions that are beyond the conventional
paradigm of fluctuations of a symmetry breaking order parameter are challenging
for theory. These phase transitions often involve emergent deconfined gauge
fields at the critical points as demonstrated in 2+1-dimensions. Examples
include phase transitions in quantum magnetism as well as those between
Symmetry Protected Topological phases. In this paper, we present several
examples of Deconfined Quantum Critical Points (DQCP) between Symmetry
Protected Topological phases in 3+1-D for both bosonic and fermionic systems.
Some of the critical theories can be formulated as non-abelian gauge theories
either in their Infra-Red free regime, or in the conformal window when they
flow to the Banks-Zaks fixed points. We explicitly demonstrate several
interesting quantum critical phenomena. We describe situations in which the
same phase transition allows for multiple universality classes controlled by
distinct fixed points. We exhibit the possibility - which we dub "unnecessary
quantum critical points" - of stable generic continuous phase transitions
within the same phase. We present examples of interaction driven band-theory-
forbidden continuous phase transitions between two distinct band insulators.
The understanding we develop leads us to suggest an interesting possible 3+1-D
field theory duality between SU(2) gauge theory coupled to one massless adjoint
Dirac fermion and the theory of a single massless Dirac fermion augmented by a
decoupled topological field theory.Comment: 83 pages, 10 figure
Emergence: Key physical issues for deeper philosophical inquiries
A sketch of three senses of emergence and a suggestive view on the emergence
of time and the direction of time is presented. After trying to identify which
issues philosophers interested in emergent phenomena in physics view as
important I make several observations pertaining to the concepts, methodology
and mechanisms required to understand emergence and describe a platform for its
investigation. I then identify some key physical issues which I feel need be
better appreciated by the philosophers in this pursuit. I end with some
comments on one of these issues, that of coarse-graining and persistent
structures.Comment: 16 pages. Invited Talk at the Heinz von Foerster Centenary
International Conference on Self-Organization and Emergence: Emergent Quantum
Mechanics (EmerQuM11). Nov. 10-13, 2011, Vienna, Austria. Proceedings to
appear in J. Phys. (Conf. Series
Emergence: Key physical issues for deeper philosophical inquiries
A sketch of three senses of emergence and a suggestive view on the emergence
of time and the direction of time is presented. After trying to identify which
issues philosophers interested in emergent phenomena in physics view as
important I make several observations pertaining to the concepts, methodology
and mechanisms required to understand emergence and describe a platform for its
investigation. I then identify some key physical issues which I feel need be
better appreciated by the philosophers in this pursuit. I end with some
comments on one of these issues, that of coarse-graining and persistent
structures.Comment: 16 pages. Invited Talk at the Heinz von Foerster Centenary
International Conference on Self-Organization and Emergence: Emergent Quantum
Mechanics (EmerQuM11). Nov. 10-13, 2011, Vienna, Austria. Proceedings to
appear in J. Phys. (Conf. Series
Self-Referential Noise and the Synthesis of Three-Dimensional Space
Generalising results from Godel and Chaitin in mathematics suggests that
self-referential systems contain intrinsic randomness. We argue that this is
relevant to modelling the universe and show how three-dimensional space may
arise from a non-geometric order-disorder model driven by self-referential
noise.Comment: Figure labels correcte
Emergence and Reduction Combined in Phase Transitions
In another paper (Butterfield 2011), one of us argued that emergence and
reduction are compatible, and presented four examples illustrating both. The
main purpose of this paper is to develop this position for the example of phase
transitions. We take it that emergence involves behaviour that is novel
compared with what is expected: often, what is expected from a theory of the
system's microscopic constituents. We take reduction as deduction, aided by
appropriate definitions. Then the main idea of our reconciliation of emergence
and reduction is that one makes the deduction after taking a limit of an
appropriate parameter . Thus our first main claim will be that in some
situations, one can deduce a novel behaviour, by taking a limit .
Our main illustration of this will be Lee-Yang theory. But on the other hand,
this does not show that the limit is physically real. For our second
main claim will be that in such situations, there is a logically weaker, yet
still vivid, novel behaviour that occurs before the limit, i.e. for finite .
And it is this weaker behaviour which is physically real. Our main illustration
of this will be the renormalization group description of cross-over phenomena.Comment: 24 pp, v2: one minor change. Contribution to the Frontiers of
Fundamental Physics (FFP 11) Conference Proceeding
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