scholarly journals Choreographed entanglement dances: Topological states of quantum matter

Science ◽  
2019 ◽  
Vol 363 (6429) ◽  
pp. eaal3099 ◽  
Author(s):  
Xiao-Gang Wen
Keyword(s):  
Symmetry Breaking ◽  
Emergent Properties ◽  
Topological Phases ◽  
Topological Order ◽  
Zero Temperature ◽  
Quantum Matter ◽  
Topological States ◽  
Basic Concepts ◽  
Symmetry Protected

It has long been thought that all different phases of matter arise from symmetry breaking. Without symmetry breaking, there would be no pattern, and matter would be featureless. However, it is now clear that for quantum matter at zero temperature, even symmetric disordered liquids can have features, giving rise to topological phases of quantum matter. Some of the topological phases are highly entangled (that is, have topological order), whereas others are weakly entangled (that is, have symmetry-protected trivial order). This Review provides a brief summary of these zero-temperature states of matter and their emergent properties, as well as their importance in unifying some of the most basic concepts in nature.

scholarly journals Topological Order: From Long-Range Entangled Quantum Matter to a Unified Origin of Light and Electrons

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Xiao-Gang Wen
Keyword(s):  
Symmetry Breaking ◽  
Long Range ◽  
Topological Order ◽  
Fractional Statistics ◽  
Microscopical Level ◽  
Macroscopic Level ◽  
Emergent Phenomena ◽  
Quantum Matter ◽  
Ordered Phases ◽  
Zero Viscosity

We review the progress in the last 20–30 years, during which we discovered that there are many new phases of matter that are beyond the traditional Landau symmetry breaking theory. We discuss new “topological” phenomena, such as topological degeneracy that reveals the existence of those new phases—topologically ordered phases. Just like zero viscosity defines the superfluid order, the new “topological” phenomena define the topological order at macroscopic level. More recently, we found that at the microscopical level, topological order is due to long-range quantum entanglements. Long-range quantum entanglements lead to many amazing emergent phenomena, such as fractional charges and fractional statistics. Long-range quantum entanglements can even provide a unified origin of light and electrons; light is a fluctuation of long-range entanglements, and electrons are defects in long-range entanglements.

scholarly journals Topological Order, Mixed States and Open Systems

2019 ◽  
Vol 26 (03) ◽  
pp. 1950012 ◽  
Author(s):  
Manuel Asorey ◽  
Paolo Facchi ◽  
Giuseppe Marmo
Keyword(s):  
Open Systems ◽  
Quantum Systems ◽  
Topological Phases ◽  
Topological Order ◽  
Mixed States ◽  
Quantum Matter ◽  
Physical Role ◽  
Topological Quantum ◽  
Pure States

The role of mixed states in topological quantum matter is less known than that of pure quantum states. Generalisations of topological phases appearing in pure states have received attention in the literature only quite recently. In particular, it is still unclear whether the generalisation of the Aharonov–Anandan phase for mixed states due to Uhlmann plays any physical role in the behaviour of the quantum systems. We analyse, from a general viewpoint, topological phases of mixed states and the robustness of their invariance. In particular, we analyse the role of these phases in the behaviour of systems with periodic symmetry and their evolution under the influence of an environment preserving its crystalline symmetries.

scholarly journals Hall viscosity, topological states and effective theories

2014 ◽  
Vol 28 (15) ◽  
pp. 1430007 ◽  
Author(s):  
Carlos Hoyos
Keyword(s):  
Transport Coefficient ◽  
Hall Conductivity ◽  
Topological Phases ◽  
Topological Order ◽  
Topological States ◽  
Effective Theories ◽  
Hall Viscosity ◽  
Galilean Invariant

Hall viscosity is a dissipationless transport coefficient whose value is quantized in units of the density in some topological phases and may be used as a measure of topological order. I give an overview of the Hall viscosity, its relation to Hall conductivity in Galilean invariant theories and its realization in effective theories.

scholarly journals Hidden symmetry-breaking picture of symmetry-protected topological order

2013 ◽  
Vol 88 (8) ◽  
Author(s):  
Dominic V. Else ◽  
Stephen D. Bartlett ◽  
Andrew C. Doherty
Keyword(s):  
Symmetry Breaking ◽  
Topological Order ◽  
Hidden Symmetry ◽  
Symmetry Protected

scholarly journals Resilience of the topological phases to frustration

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Vanja Marić ◽  
Fabio Franchini ◽  
Domagoj Kuić ◽  
Salvatore Marco Giampaolo
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary Conditions ◽  
Topological Phases ◽  
Topological Order ◽  
Different Boundary Conditions ◽  
One Dimensional ◽  
Magnetic Orders ◽  
Symmetry Protected ◽  
Antiferromagnetic Spin ◽  
Peculiar Behavior

AbstractRecently it was highlighted that one-dimensional antiferromagnetic spin models with frustrated boundary conditions, i.e. periodic boundary conditions in a ring with an odd number of elements, may show very peculiar behavior. Indeed the presence of frustrated boundary conditions can destroy the local magnetic orders presented by the models when different boundary conditions are taken into account and induce novel phase transitions. Motivated by these results, we analyze the effects of the introduction of frustrated boundary conditions on several models supporting (symmetry protected) topological orders, and compare our results with the ones obtained with different boundary conditions. None of the topological order phases analyzed are altered by this change. This observation leads naturally to the conjecture that topological phases of one-dimensional systems are in general not affected by topological frustration.

scholarly journals Persistence of topological phases in non-Hermitian quantum walks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Vikash Mittal ◽  
Aswathy Raj ◽  
Sanjib Dey ◽  
Sandeep K. Goyal
Keyword(s):  
Quantum Walk ◽  
Quantum Walks ◽  
Topological Phases ◽  
Topological Order ◽  
Topological Phase ◽  
Two Dimensional ◽  
One Dimensional ◽  
Topological Phase Transition ◽  
Topological States ◽  
Time Quantum

AbstractDiscrete-time quantum walks are known to exhibit exotic topological states and phases. Physical realization of quantum walks in a lossy environment may destroy these phases. We investigate the behaviour of topological states in quantum walks in the presence of a lossy environment. The environmental effects in the quantum walk dynamics are addressed using the non-Hermitian Hamiltonian approach. We show that the topological phases of the quantum walks are robust against moderate losses. The topological order in one-dimensional split-step quantum walk persists as long as the Hamiltonian respects exact $${{\mathcal {P}}}{{\mathcal {T}}}$$ P T -symmetry. Although the topological nature persists in two-dimensional quantum walks as well, the $${{\mathcal {P}}}{{\mathcal {T}}}$$ P T -symmetry has no role to play there. Furthermore, we observe topological phase transition in two-dimensional quantum walks that is induced by losses in the system.

scholarly journals Quark confinement and the renormalization group

2011 ◽  
Vol 369 (1946) ◽  
pp. 2718-2734 ◽  
Author(s):  
Michael C. Ogilvie
Keyword(s):  
Renormalization Group ◽  
Symmetry Breaking ◽  
Scaling Laws ◽  
Dyson Equation ◽  
String Tension ◽  
Real Space ◽  
Equation Approach ◽  
Zero Temperature ◽  
Quark Confinement ◽  
Basic Concepts

Recent approaches to quark confinement are reviewed, with an emphasis on their connection to renormalization group (RG) methods. Basic concepts related to confinement are introduced: the string tension, Wilson loops and Polyakov lines, string breaking, string tension scaling laws, centre symmetry breaking and the deconfinement transition at non-zero temperature. Current topics discussed include confinement on R 3 × S 1 , the real-space RG, the functional RG and the Schwinger–Dyson equation approach to confinement.

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