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Manipulating topology of quantum phase transitions by symmetry enhancement

Oct 7, 2024

6 pages

e-Print:

2410.05059 [cond-mat.str-el]

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Abstract: (arXiv)

Topology plays a cardinal role in explaining phases and quantum phase transitions beyond the Landau-Ginzburg-Wilson paradigm. In this study, we formulate a set of models of Dirac fermions in 2+1 dimensions with SU(

N

)

\times

SU(2)

\times

U(1) symmetry that have the potential to host critical points described by field theories with topological terms. For

N=2

it shows a rich phase diagram containing semimetallic, quantum spin Hall insulating, Kekulé valence bond solid and s-wave superconducting phases and features multiple Landau-Ginzburg-Wilson phase transitions driven by interaction strength. At

N=1

a deconfined quantum critical point is observed. At

N=2

one expects the critical theory to correspond to a level 2 Wess-Zumino-Witten theory in 2+1 dimensions. Here the numerical results however show a strong first order transition. Another transition can be governed by a topological

\theta

-term which is rendered irrelevant for even values of

N

thus leading to Landau-Ginzburg-Wilson behaviour.

Note:

6 pages main text + 7 pages Supplemental Material, 3 figures main text + 9 figures Supplemental Material

References(72)

Figures(21)

[1]

Journal of Physics C:

J.M. Kosterlitz
,
D.J. Thouless

- Solid State Phys. 6 (1973) 1181

[2]

Nonlinear field theory of large spin Heisenberg antiferromagnets. Semiclassically quantized solitons of the one-dimensional easy Axis Neel state

F.D.M. Haldane
(
- Southern California U.
)

- Phys.Rev.Lett. 50 (1983) 1153-1156
•
DOI:
- 10.1103/PhysRevLett.50.1153

[3]

Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm

- Phys.Rev.B 70 (2004) 14, 144407
•
DOI:
- 10.1103/PhysRevB.70.144407

[4]

J.E. Moore

- Nature 464 (2010) 194

[5]

Spin liquids in frustrated magnets

Leon Balents

- Nature 464 (2010) 7286, 199-208
•
DOI:
- 10.1038/nature08917

[6]

E. Dagotto
,
T.M. Rice

- Science 271 (1996) 618
•
- http://science.sciencemag.org/content/271/5249/618.full.pdf

[7]

On Next‐Nearest‐Neighbor Interaction in Linear Chain. I

- J.Math.Phys. 10 (1969) 8, 1388
•
DOI:
- 10.1063/1.1664978

[8]

Numerical evidence for multiplicative logarithmic corrections from marginal operators

Sebastian Eggert
(
- Goteborg, ITP
)

- Phys.Rev.B 54 (1996) R9612
•
e-Print:
- cond-mat/9602026
•
DOI:
- 10.1103/PhysRevB.54.R9612

[9]

Critical Theory of Quantum Spin Chains

Ian Affleck
(
- Princeton U.
)
,
F.D.M. Haldane
(
- UC, San Diego
)

- Phys.Rev.B 36 (1987) 5291-5300
•
DOI:
- 10.1103/PhysRevB.36.5291

[10]

Kavli Institute for Theoretical Physics. Audiovisual

T. Senthil

•
DOI:
- 10.26081/K6X70N

[11]

From ${SU (2)}_{5}$ to ${SU (2)}_{3}$ Wess-Zumino-Witten transitions in a frustrated spin- $\frac{5}{2}$ chain

- Phys.Rev.B 105 (2022) 17, 174402
•
e-Print:
- 2202.05087
•
DOI:
- 10.1103/PhysRevB.105.174402

[12]

O (3) Nonlinear sigma Model and the Topological Distinction between Integer- and Half-Integer-Spin Antiferromagnets in Two Dimensions

F.D.M. Haldane
(
- UC, San Diego
)

- Phys.Rev.Lett. 61 (1988) 1029-1032
•
DOI:
- 10.1103/PhysRevLett.61.1029

[13]

Some Features of the Phase Diagram of the Square Lattice SU( $N$ ) Antiferromagnet

N. Read
(
- Yale U.
)
,
S. Sachdev
(
- Yale U.
)

- Nucl.Phys.B 316 (1989) 609-640
•
DOI:
- 10.1016/0550-3213(89)90061-8

[14]

Phase diagram of the $SU (N)$ antiferromagnet of spin $S$ on a square lattice

- Phys.Rev.B 108 (2023) 11, 115151
•
e-Print:
- 2304.07329
•
DOI:
- 10.1103/PhysRevB.108.115151

[15]

Deconfined Quantum Critical Points

T. Senthil
(
- MIT
)
,
Ashvin Vishwanath
(
- MIT
)
,
Leon Balents
(
- UC, Santa Barbara
)
,
Subir Sachdev
(
- Yale U.
)
,
Matthew P.A. Fisher
(
- Santa Barbara, KITP
)

- Science 303 (2004) 5663, 1490-1494
•
e-Print:
- cond-mat/0311326
•
DOI:
- 10.1126/science.1091806

[16]

Competing orders, non-linear sigma models, and topological terms in quantum magnets

T. Senthil
(
- Bangalore, Indian Inst. Sci. and
- MIT, LNS
)
,
Matthew P.A. Fisher
(
- Santa Barbara, KITP
)

- Phys.Rev.B 74 (2006) 064405
•
e-Print:
- cond-mat/0510459
•
DOI:
- 10.1103/PhysRevB.74.064405

[17]

Many-Body Spin Berry Phases Emerging from the $\pi$ -Flux State: Competition between Antiferromagnetism and the Valence-Bond-Solid State

- Phys.Rev.Lett. 95 (2005) 3, 036402
•
e-Print:
- cond-mat/0501365
•
DOI:
- 10.1103/PhysRevLett.95.036402

[18]

Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry

- Phys.Rev.Lett. 119 (2017) 19, 197203
•
e-Print:
- 1707.03027
•
DOI:
- 10.1103/PhysRevLett.119.197203

[19]

Theta terms in nonlinear sigma models

A.G. Abanov
(
- MIT
)
,
P.B. Wiegmann
(
- Chicago U., EFI and
- Landau Inst.
)

- Nucl.Phys.B 570 (2000) 685-698
•
e-Print:
- hep-th/9911025
•
DOI:
- 10.1016/S0550-3213(99)00820-2

[20]

Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions

Anders W. Sandvik

- Phys.Rev.Lett. 98 (2007) 22, 227202
•
e-Print:
- cond-mat/0611343
•
DOI:
- 10.1103/PhysRevLett.98.227202

[21]

Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models

Adam Nahum
(
- MIT, Cambridge, Dept. Phys.
)
,
J.T. Chalker
(
- Oxford U., Theor. Phys.
)
,
P. Serna
(
- Oxford U., Theor. Phys. and
- Murcia U.
)
,
M. Ortuño
(
- Murcia U.
)
,
A.M. Somoza
(
- Murcia U.
)

- Phys.Rev.X 5 (2015) 4, 041048
•
e-Print:
- 1506.06798
•
DOI:
- 10.1103/PhysRevX.5.041048

[22]

Emergent SO(5) Symmetry at the Néel to Valence-Bond-Solid Transition

Adam Nahum
(
- MIT, Cambridge, Dept. Phys.
)
,
P. Serna
(
- Oxford U., Theor. Phys.
)
,
J.T. Chalker
(
- Oxford U., Theor. Phys.
)
,
M. Ortuño
(
- Murcia U.
)
,
A.M. Somoza
(
- Murcia U.
)

- Phys.Rev.Lett. 115 (2015) 26, 267203
•
e-Print:
- 1508.06668
•
DOI:
- 10.1103/PhysRevLett.115.267203

[23]

Superconductivity from the Condensation of Topological Defects in a Quantum Spin-Hall Insulator

Yuhai Liu
(
- Beijing Normal U.
)
,
Zhenjiu Wang
(
- Wurzburg U.
)
,
Toshihiro Sato
(
- Wurzburg U.
)
,
Martin Hohenadler
(
- Wurzburg U.
)
,
Chong Wang
(
- Perimeter Inst. Theor. Phys.
)

et al.

- Nature Commun. 10 (2019) 1, 2658
•
e-Print:
- 1811.02583
•
DOI:
- 10.1038/s41467-019-10372-0

[24]

Phases and exotic phase transitions of a two-dimensional Su-Schrieffer-Heeger model

- Phys.Rev.B 109 (2024) 19, 195154
•
e-Print:
- 2307.07613
•
DOI:
- 10.1103/PhysRevB.109.195154

[25]

Wess-Zumino-Witten terms in graphene Landau levels

Junhyun Lee
(
- Harvard U.
)
,
Subir Sachdev
(
- Harvard U. and
- Perimeter Inst. Theor. Phys.
)

- Phys.Rev.Lett. 114 (2015) 22, 226801
•
e-Print:
- 1411.5684
•
DOI:
- 10.1103/PhysRevLett.114.226801

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