Geometric phases for mixed states of the Kitaev chain

Ole Andersson; Ingemar Bengtsson; Marie Ericsson; Erik Sjöqvist

doi:10.1098/rsta.2015.0231

Geometric phases for mixed states of the Kitaev chain

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2015.0231 ◽

2016 ◽

Vol 374 (2068) ◽

pp. 20150231 ◽

Cited By ~ 13

Author(s):

Ole Andersson ◽

Ingemar Bengtsson ◽

Marie Ericsson ◽

Erik Sjöqvist

Keyword(s):

Finite Temperature ◽

Geometric Phase ◽

Berry Phase ◽

Condensed Matter ◽

Order Parameters ◽

Topological Order ◽

Mixed States ◽

Geometric Phases

The Berry phase has found applications in building topological order parameters for certain condensed matter systems. The question whether some geometric phase for mixed states can serve the same purpose has been raised, and proposals are on the table. We analyse the intricate behaviour of Uhlmann's geometric phase in the Kitaev chain at finite temperature, and then argue that it captures quite different physics from that intended. We also analyse the behaviour of a geometric phase introduced in the context of interferometry. For the Kitaev chain, this phase closely mirrors that of the Berry phase, and we argue that it merits further investigation.

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GEOMETRIC PHASES AND QUANTUM PHASE TRANSITIONS

International Journal of Modern Physics B ◽

10.1142/s0217979208038855 ◽

2008 ◽

Vol 22 (06) ◽

pp. 561-581 ◽

Cited By ~ 31

Author(s):

SHI-LIANG ZHU

Keyword(s):

Phase Transitions ◽

Geometric Phase ◽

Quantum Phase Transitions ◽

Condensed Matter ◽

Quantum Phase ◽

Many Body ◽

Scientific Communities ◽

Geometric Phases ◽

Many Body Systems ◽

The Many

Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant relation was recognized before recent work. In this paper, we present a review of the connection recently established between these two interesting fields: investigations in the geometric phase of the many-body systems have revealed the so-called "criticality of geometric phase", in which the geometric phase associated with the many-body ground state exhibits universality, or scaling behavior in the vicinity of the critical point. In addition, we address the recent advances on the connection of some other geometric quantities and quantum phase transitions. The closed relation recently recognized between quantum phase transitions and some of the geometric quantities may open attractive avenues and fruitful dialogue between different scientific communities.

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BERRY PHASE IN COUPLED TWO-LEVEL SYSTEMS

Modern Physics Letters B ◽

10.1142/s0217984913500887 ◽

2013 ◽

Vol 27 (12) ◽

pp. 1350088 ◽

Cited By ~ 2

Author(s):

X. Y. ZHANG ◽

J. H. TENG ◽

X. X. YI

Keyword(s):

Asymptotic Behavior ◽

Geometric Phase ◽

Berry Phase ◽

External Control ◽

Control Parameters ◽

Coupling Constant ◽

Geometric Phases ◽

Coupled Subsystems ◽

Two Level Systems ◽

The Individual

The application of geometric phases into robust control of quantal systems has triggered exploration of the geometric phase for coupled subsystems. Earlier studies have mainly focused on the situation where the external control parameters are in the free Hamiltonian of the subsystems, i.e. the controls exert only on the individual subsystems. Here we consider another circumstance that we can control the coupling geiϕ between the subsystems. By changing only the phase ϕ in the coupling constant, we derive the Berry phase acquired by the system and compare it to the geometric phase acquired by changing the coupling strength g. We find that the asymptotic behavior of the Berry phase depends on the relative Rabi frequency of the two subsystems, and it approaches π when the amplitude of the coupling tends to infinity.

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GEOMETRIC PHASES OF PURE AND MIXED STATES

COSMOS ◽

10.1142/s0219607706000183 ◽

2006 ◽

Vol 02 (01) ◽

pp. 81-100

Author(s):

R. RAVISHANKAR ◽

J. F. DU

Keyword(s):

Experimental Measurement ◽

Mixed State ◽

Geometric Phase ◽

Mixed States ◽

Geometric Phases

The purpose of this article is to review the literature for pure and mixed state geometric phase and also the experimental measurement of the phase using NMR.

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Genuine vacuum-induced geometric phases

Modern Physics Letters B ◽

10.1142/s0217984915500438 ◽

2015 ◽

Vol 29 (11) ◽

pp. 1550043 ◽

Cited By ~ 1

Author(s):

Minghao Wang ◽

L. F. Wei ◽

J. Q. Liang

Keyword(s):

Excited State ◽

Quantum Electrodynamics ◽

Geometric Phase ◽

Berry Phase ◽

Cavity Quantum Electrodynamics ◽

Vacuum Field ◽

Geometric Phases ◽

Field System ◽

The One

Since a pioneer work on vacuum-induced Berry phase (VIBP) was done by Fuentes-Guridi et al. [Phys. Rev. Lett. 89 (2002) 220404], much attention has been paid to the geometric phase effects of vacuum field. However, all the so-called VIBPs investigated previously are not purely vacuum-induced (i.e. the nonvacuum components of the field are also involved). In this paper, we discuss how to deliver geometric phases from the evolution of a genuine vacuum field in a standard cavity quantum electrodynamics (QED) system. First, we design a cyclic evolution of an atom–field system with the atom being initially prepared at the excited state and the field at the genuine vacuum. Then, we calculate the geometric phases acquired during such a cyclic evolution. It is found that such geometric phases are really induced by an evolution of the genuine vacuum field. Specifically, our generic proposal is demonstrated with both the one- and two-mode Jaynes–Cummings model interactions (JCM).

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Observation of twist-induced geometric phases and inhibition of optical tunneling via Aharonov-Bohm effects

Science Advances ◽

10.1126/sciadv.aau8135 ◽

2019 ◽

Vol 5 (1) ◽

pp. eaau8135 ◽

Cited By ~ 2

Author(s):

Midya Parto ◽

Helena Lopez-Aviles ◽

Jose E. Antonio-Lopez ◽

Mercedeh Khajavikhan ◽

Rodrigo Amezcua-Correa ◽

...

Keyword(s):

Geometric Phase ◽

Berry Phase ◽

Polarization State ◽

Guided Wave ◽

Physical Sciences ◽

Solid State Physics ◽

Fiber System ◽

Geometric Phases ◽

Photon Tunneling ◽

Aharonov Bohm

Geometric phases appear ubiquitously in many and diverse areas of the physical sciences, ranging from classical and molecular dynamics to quantum mechanics and solid-state physics. In the realm of optics, similar phenomena are known to emerge in the form of a Pancharatnam-Berry phase whenever the polarization state traces a closed contour on the Poincaré sphere. While this class of geometric phases has been extensively investigated in both free-space and guided wave systems, the observation of similar effects in photon tunneling arrangements has so far remained largely unexplored. Here, we experimentally demonstrate that the tunneling or coupling process in a twisted multicore fiber system can display a chiral geometric phase accumulation, analogous to the Aharonov-Bohm effect. In our experiments, the tunneling geometric phase is manifested through the interference of the corresponding supermodes. Our work provides the first observation of Aharonov-Bohm suppression of tunneling in an optical setting.

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Interface-induced sign reversal of the anomalous Hall effect in magnetic topological insulator heterostructures

Nature Communications ◽

10.1038/s41467-020-20349-z ◽

2021 ◽

Vol 12 (1) ◽

Cited By ~ 1

Author(s):

Fei Wang ◽

Xuepeng Wang ◽

Yi-Fan Zhao ◽

Di Xiao ◽

Ling-Jie Zhou ◽

...

Keyword(s):

Hall Effect ◽

Electric Fields ◽

First Principles ◽

Berry Phase ◽

Condensed Matter ◽

Anomalous Hall Effect ◽

First Principles Calculations ◽

Sign Reversal ◽

Berry Curvature ◽

Topological Materials

AbstractThe Berry phase picture provides important insights into the electronic properties of condensed matter systems. The intrinsic anomalous Hall (AH) effect can be understood as the consequence of non-zero Berry curvature in momentum space. Here, we fabricate TI/magnetic TI heterostructures and find that the sign of the AH effect in the magnetic TI layer can be changed from being positive to negative with increasing the thickness of the top TI layer. Our first-principles calculations show that the built-in electric fields at the TI/magnetic TI interface influence the band structure of the magnetic TI layer, and thus lead to a reconstruction of the Berry curvature in the heterostructure samples. Based on the interface-induced AH effect with a negative sign in TI/V-doped TI bilayer structures, we create an artificial “topological Hall effect”-like feature in the Hall trace of the V-doped TI/TI/Cr-doped TI sandwich heterostructures. Our study provides a new route to create the Berry curvature change in magnetic topological materials that may lead to potential technological applications.

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