Vivian de la Incera Sharif University of Technology Webinar August - - PowerPoint PPT Presentation

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Vivian de la Incera Sharif University of Technology Webinar August - - PowerPoint PPT Presentation

Nov 04, 2022 22 likes β€’352 views

Magnetic Dual Chiral Density Wave Phase of Dense Quark Matter: Properties and Relevance for Neutron Stars Vivian de la Incera Sharif University of Technology Webinar August 4, 2020 1 Outline 1. Why Quark Matter? 2.Why Inhomogeneous?

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Vivian de la Incera

Sharif University of Technology Webinar August 4, 2020

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Magnetic Dual Chiral Density Wave Phase

  • f Dense Quark Matter:

Properties and Relevance for Neutron Stars

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Outline

  • 1. Why Quark Matter?

2.Why Inhomogeneous? 3.Basics of the MDCDW Phase 4.MDCDW: a Prospect for NS Core Phases

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Matter under Extreme Conditions

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  • 1. Why a Quark Matter Phase?
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Composition of Matter in NS

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Annala et al., Nature Physics 2020

Range of Allowed NS EoS

Obtained using multiple interpolation methods and two astrophysical constraints:

  • EoS supports ~1.97 π‘βŠ™
  • Tidal deformability

70 < Ξ›(1.4 π‘βŠ™)< 580

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Quark Matter is Rather Standard

Annala et al., Nature Physics 2020

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PulsarΚΌs surface: B ~ 1012–1014G Magnetars: Surface: B ~ 1015–1016G Core: 1016G < B ≀ 1018G

B is quite Ubiquitous

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  • 2. Why Inhomogeneous?
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Approaching Intermediate Densities From Both Sides

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It pairs particle and antiparticle with

  • pposite spin and momentum

(homogeneous condensate)

Cooper Pairing Chiral Condensate

Main channel pairs (all) quarks of different flavors and colors with

  • pposite spins and momenta. Favored at

asymptotically high densities.

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Approaching Intermediate Densities From Both Sides

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It pairs particle and antiparticle with

  • pposite spin and momentum

(homogeneous condensate) Main channel pairs quarks of different flavors with opposite spins and momenta. Favored at very high densities.

Cooper Pairing Chiral Condensate

A Way out: Spatially Modulated Chiral Condensates A Way out: Spatially Modulated Quark-Quark Condensates Not favored with increasing density Suffers from Fermi surface mismatch with decreasing densities leading to chromomagnetic instabilities.

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Density Wave Pairing

It pairs particle and hole with opposite spin and parallel momenta (nonzero net momentum) No Fermi surface mismatch Favored over homogeneous chiral condensate Favored over CS at large Nc

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  • 3. Basics of the MDCDW Phase
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Magnetic Dual Chiral Density Wave Model

2-flavor NJL model + QED at finite baryon density and with magnetic field Bβˆ₯ 𝑨 It favors the formation of an inhomogeneous chiral condensate Mean-field Lagrangian

Frolov, et al PRD82,’10 Tatsumi et al PLB743,’15

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Magnetic Dual Chiral Density Wave Model

2-flavor NJL model + QED at finite baryon density and with magnetic field Bβˆ₯ 𝑨 It favors the formation of an inhomogeneous chiral condensate Mean-field Lagrangian

Complex mass term

Frolov, et al PRD82,’10 Tatsumi et al PLB743,’15

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Chiral Transformation and Asymmetric Spectrum

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LLL mode is Asymmetric! Performing the chiral transformation The MF Lagrangian acquires a mass term plus a 𝛿"𝛿# term in the derivative The corresponding fermion spectrum is

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Nontrivial Topology of the MDCDW Phase

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The anomaly makes the MDCDW solution energetically favored over the homogeneous condensate Topology emerges due to the LLL spectral asymmetry

Anomalous baryon number density

Frolov, et al PRD82,’10

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Axion Term

Ferrer & VI, PLB’ 2017; NPB’ 2018

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Key observation: the fermion measure is not invariant under UA πœ„=$%

&

πœ† = 𝑓! 2𝜌!

The effective MF Lagrangian acquires an axion term: Integrating out the fermions, we find the electromagnetic effective action in the MDCDW model

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QED in MDCDW is Axion QED

Anomalous charge Dissipationless Hall current βŠ₯ to both B and E

Ferrer & VI, Phys.Lett. B769 (2017) 208; Nucl.Phys. B931 (2018) 192 Anomalous Hall conductivity

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  • 4. Can MDCDW be a viable Prospect

for NS Core Phases?

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Test #1: Stability against Fluctuations

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Low-energy Theory

Order Parameter

The low-energy theory is described by a generalized GL expansion of the thermodynamic potential in powers of the order parameter and its derivatives. The resulting expansion is invariant under the symmetries of the

  • riginal theory in a B

UV(1)xUA(1)xSO(2)xR3

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GL Expansion

Low Energy GL Expansion of the MDCDW Free Energy

Ferrer & VI, PRDβ€˜2020

MDCDW ansatz The b coefficients are a consequence of the asymmetry of the LLL spectrum The 𝑏",$

(&)

coefficients are a consequence of having an external vector

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GL Expansion

Low Energy GL Expansion of the MDCDW Free Energy

Ferrer & VI, PRDβ€˜2020

MDCDW ansatz The b coefficients are a consequence of the asymmetry of the LLL spectrum The 𝑏",$

(&)

coefficients are a consequence of having an external vector

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Spontaneous Breaking of Chiral and Translational Symmetries

# 𝑁 𝑨 = 𝑛𝑓'()

with m and q solutions of the stationary equations:

Symmetry is reduced to UV(1)xSO(2)xR2 Fluctuations of the condensate come from two Goldstone Bosons: pions and phonons

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Low-Energy Theory of Fluctuations

Chiral and translation transformations are locked The phonon free energy is then

Anisotropic spectrum

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Stability against the Fluctuations

Finite! Thanks to B there are no soft transverse modes, hence no Landau-Peierls instability. The MDCDW phase is stable against thermal fluctuations.

In contrast at B=0

Infrared divergent. Any finite T no matter how small destroy the long-range order

Ferrer & VI, PRDβ€˜2020

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Test #2: 2 π‘βŠ™

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Carignano, Ferrer, VI, Paulucci, PRD 2015

Electrically Neutral MDCDW Phase

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Test #3: Thermal Properties

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Work in Progress

Cummings et. al PRC’2017

Lower limit of NS core heat capacity established from transiently-accreting NS is violated by CFL But not by MDCDW . Paper coming soon…

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MDCDW Weyl Semimetals

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Ξ  Described by Dirac Hamiltonian Topology is associated to asymmetry of the LLL states in the MDCDW .

Ferrer and VI, β€˜15,’17,’18

Described by Dirac Hamiltonian Axion term in the electromagnetic action Axion term in the electromagnetic action Anomalous Hall conductivity

Anomalous Hall conductivity

Topology is associated to band structure with nodes of opposite chirality separated by 2b in momentum space

Burkov, ’17

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Summary:

  • MDCDW is a viable phase at intermediate

densities

  • So far is compatible with several

astrophysical constraints

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  • Need to Connect to more Measurable NS
  • bservables that can confirm/falsify proposed

intermediate density candidates: MDCDW, Quarkyonic, CS Phases.

  • More studies on consequences of the topological

properties

Outlook: