Current-driven Tricritical Point in Large-Nc Gauge Theory Shin - - PowerPoint PPT Presentation

Current-driven Tricritical Point in Large-Nc Gauge Theory

Shin Nakamura (Chuo U.)

Strings and Fields 2020, YITP Nov. 16th, 2020

• Ref. [T. Imaizumi, M. Matsumoto and S.N., PRL124 (2020) 19, 191603]

Poster #10

Motivation

One direction to explore new physics: introduction of new parameters into the phase diagram.

𝐾

My question: Any new phenomena in the presence of current?

𝐾 : electric current as a new parameter

• f the phase diagram.

Phase diagram: summary of macroscopic states of systems

𝜈 𝑈

Why current?

Nature of materials in the presence of 𝐾 is not yet understood well. When 𝐾 and 𝐹 are constant, the system is in a Non-equilibrium Steady State (NESS).

𝜈 𝑈 𝐾

• Any new phase structure in NESS?
• Any new phenomena in NESS?

𝐾 is rather new:

Because, 𝐾 ∙ 𝐹 produces heat and entropy.

• ut of equilibrium

Extension of phase diagram into NESS.

Nonequilibrium

http://www.ss.scphys.kyoto-u.ac.jp/kibanS_h29-33/en/event.html

Any new phenomena in the presence of current?

This question is shared with researchers including experimental physicists.

In this talk,

We find a novel TCP (tricritical point) that is realized only in the presence of 𝐾.

[T. Imaizumi, M. Matsumoto and S.N., PRL124 (2020) 19, 191603]

Broken phase Symmetric phase 𝐶gap

TCP

(I will explain the details of this figure later.)

What is TCP?

A point at which three-phase coexistence terminates.

TCP

CP Our case: 𝑄 → 𝐾

2nd-order line 1st-order line

𝑄 𝑆

TCP

When 𝑅 = 0

𝑄 𝑆

2nd-order point 1st-order line

𝑄 𝑅 𝑆

2nd-order line 1st-order surface triple line: 3-phase coexistence

3d phase diagram with parameters 𝑄, 𝑅 and 𝑆.

We employ holography

Because we can attack non-equilibrium physics. An advantage of holography In holography, the expectation values are obtained (by GKP-W) once we have the dual geometry.

Microscopic theory Macroscopic quantity Expectation value of physical quantity

Coarse graining Connection between UV and IR.

It has already been “encoded” in the geometry.

Our system

Our system: 𝑛 ≠ 0 with 𝐹𝑦 𝐾𝑦 , 𝐶𝑨 at 𝑈 .

𝑇𝑉(𝑂𝑑) 𝒪 = 4 SYM + 𝒪 = 2 hypermultiplet of mass 𝑛 at 𝑂𝑑 ≫ 1 with 𝜇 = 𝑕YM

2 𝑂𝑑 ≫ 1 at finite temperature 𝑈.

The D3-D7 system

[Karch and Katz, 2002] Our parameters

Because of the conformal symmetry

𝑛 𝑈 , 𝐾 𝑈3 , 𝐶 𝑈2 .

“Chiral symmetry” at 𝑛 = 0:

𝑟 𝜒1 𝜒2 𝑟 If 𝑛=0, we have a global U(1) symmetry under 𝑟 → 𝑟𝑓𝑗𝛽, when ത 𝑟𝑟 = 0.

[Babington, Erdmenger, Evans, Guralnik and Kirsch, 2008]

D-brane configurations

1 2 3 4 5 6 7 8 9 D3 ○ ○ ○ ○ D7 ○ ○ ○ ○ ○ ○ ○ ○

S5 AdS5 (AdS-BH at 𝑈 > 0) S2: radius sin 𝜄

BH D7

𝑠 sin 𝜄

symmetric under a U(1) chiral symmetry. 𝑛 𝑛 ≠ 0 𝑛 = 0

𝑠 𝑠 cos 𝜄

U(1) symmetry breaking by magnetic field 𝐶

BH

𝑠 sin 𝜄

symmetric configuration

If we apply the electric field 𝐹, this “symmetry-broken conductor phase” can also be possible. The U(1) symmetry can be broken when we introduce (a strong enough) magnetic field 𝐶. [Filev et. al. 2007]

𝑠 cos 𝜄

The order parameter

BH

𝑠 sin 𝜄

1 3

( ) const. ...... sin ( ) r r mr r r r m  

− − →

= + + = The shape of the D7 is described by the function θ(r).

The global U(1) symmetry under 𝑟 → 𝑟𝑓𝑗𝛽, when ത 𝑟𝑟 = 0.

When 𝑛 = 0, the chiral condensate ത 𝑟𝑟 is given by this coefficient. Chiral condensate ത 𝑟𝑟 is the order parameter. 𝑠 cos 𝜄

Conductivity

[Karch and O’Bannon, 2007]

The nonlinear conductivity of the D3-D7 system can be computed by using the GKP-W prescription.

𝐾 = 𝜏 𝐹 𝐹

The conductivity is computed even in the presence

• f external magnetic field 𝐶.

[Ammon, Ngo and O’Bannon, 2009]

What we have observed for 𝑛 = 0

𝐶 𝐶gap

Broken phase Symmetric phase

𝑈: fixed 𝐾

Broken phase Symmetric phase 𝐶gap 1st 2nd

𝐾 1/𝐶

1st 2nd

TCP TCP TCP

What is TCP?

A point at which three-phase coexistence terminates.

TCP

CP We choose 𝑄 → 𝐾

2nd-order line 1st-order line

𝑄 𝑆

TCP

When 𝑅 = 0

𝑄 𝑆

2nd-order point 1st-order line

𝑄 𝑅 𝑆

2nd-order line 1st-order surface triple line: 3-phase coexistence

3d phase diagram with parameters 𝑄, 𝑅 and 𝑆.

The 3rd parameter: 𝑛

If 𝑛 corresponds to the 3rd parameter, crossover should be observed at 𝑛 ≠ 0.

We observed crossover.

𝑛 = 0.01

𝐾 𝐶

CP

crossover

Crossover

Our phase diagram

TCP

𝐾/𝑈3 𝑛/𝑈 𝑈2/𝐶

2nd-order line 1st-order surface triple line: 3-phase coexistence 𝐾/𝑈3

𝑈2/𝐶

2nd-order line 1st-order line

TCP

𝐾/𝑈3

𝑈2/𝐶

2nd-order point 1st-order line

CP

When 𝑛 ≠ 0

This TCP is observed only at 𝐾 ≠ 0 where the system is a NESS.

When 𝑛 = 0

Current-driven nonequilibrium TCP

Critical exponents: equilibrium case

TCP

𝑈 𝑛 𝜈

2nd-order line 1st-order surface triple line: 3-phase coexistence

Order parameter ∝ (𝑈

𝑑 − 𝑈) 𝛾

Example of equilibrium phase diagram of 2-flavor QCD.

[Halaz, Jackson, Shrock, Stephanov and Verbaarschot, 1998]

Landau theory for equilibrium systems 𝛾 = 1/2 at CP 𝛾 = 1/4 at TCP

Our case

TCP

𝐾 𝑛 1/𝐶

2nd-order line 1st-order surface triple line: 3-phase coexistence

ത 𝑟𝑟 ∝ 𝐾𝑑 − 𝐾 𝛾

Let us use 𝐾:

𝛾 = 0.4993 ≈ 1/2 at CP 𝛾 = 0.2503 ≈ 1/4 at TCP

Landau theory for equilibrium systems

𝛾 = 1/2 at CP 𝛾 = 1/4 at TCP

Summary

• We discovered a novel tricritical point (TCP) and

associated phase transitions that appear only in NESS at 𝐾 ≠ 0.

• The obtained critical exponent 𝛾 agreed with

that of the Landau theory if we replace 𝑈 of the Landau theory with 𝐾.

Further directions

• Other critical exponents? (work in progress)
• Possible observation in experiments?