Ising order in a magnetized Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya interaction

Chan, Yang-Hao; Jin, Wen; Jiang, Hong-Chen; Starykh, Oleg A.

doi:10.1103/physrevb.96.214441

Title: Ising order in a magnetized Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya interaction

Abstract

We report a combined analytical and density matrix renormalized group study of the antiferromagnetic XXZ spin-1/2 Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya (DM) interaction and a transverse magnetic eld. The numerically determined phase diagram of this model, which features two ordered Ising phases and a critical Luttinger liquid one with fully broken spin-rotational symmetry, agrees well with the predictions of Garate and Affleck [Phys. Rev. B 81, 144419 (2010)]. We also con rm the prevalence of the Nz Neel Ising order in the regime of comparable DM and magnetic field magnitudes.

Authors:

Chan, Yang-Hao ^[1]; Jin, Wen ^[2]; Jiang, Hong-Chen ^[3]; Starykh, Oleg A. ^[2]

Academia Sinica, Taipei (Taiwan)
Univ. of Utah, Salt Lake City, UT (United States)
SLAC National Accelerator Lab., Menlo Park, CA (United States)

Publication Date:: 2017-12-29

Research Org.:: SLAC National Accelerator Lab., Menlo Park, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1424745

Alternate Identifier(s):: OSTI ID: 1416441

Grant/Contract Number:: DMR-1507054; AC02-76SF00515

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 96; Journal Issue: 21; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats


                    Chan, Yang-Hao, Jin, Wen, Jiang, Hong-Chen, and Starykh, Oleg A. Ising order in a magnetized Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya interaction.  United States: N. p., 2017. 
Web.  doi:10.1103/physrevb.96.214441.

Copy to clipboard


                    Chan, Yang-Hao, Jin, Wen, Jiang, Hong-Chen, & Starykh, Oleg A. Ising order in a magnetized Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya interaction.  United States.  https://doi.org/10.1103/physrevb.96.214441

Copy to clipboard


                    Chan, Yang-Hao, Jin, Wen, Jiang, Hong-Chen, and Starykh, Oleg A. Fri .  
"Ising order in a magnetized Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya interaction".  United States.  https://doi.org/10.1103/physrevb.96.214441.  https://www.osti.gov/servlets/purl/1424745.

Copy to clipboard


                    
@article{osti_1424745,

  title        = {Ising order in a magnetized Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya interaction},

  author       = {Chan, Yang-Hao and Jin, Wen and Jiang, Hong-Chen and Starykh, Oleg A.},

  abstractNote = {We report a combined analytical and density matrix renormalized group study of the antiferromagnetic XXZ spin-1/2 Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya (DM) interaction and a transverse magnetic eld. The numerically determined phase diagram of this model, which features two ordered Ising phases and a critical Luttinger liquid one with fully broken spin-rotational symmetry, agrees well with the predictions of Garate and Affleck [Phys. Rev. B 81, 144419 (2010)]. We also con rm the prevalence of the Nz Neel Ising order in the regime of comparable DM and magnetic field magnitudes.},

  doi          = {10.1103/physrevb.96.214441},

  journal      = {Physical Review B},

  number       = 21,

  volume       = 96,

  place        = {United States},

  year         = {2017},

  month        = {12}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1103/physrevb.96.214441

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 4 works

Citation information provided by
Web of Science

Figures / Tables:

FIG. 1: Solution of Kosterlitz-Thouless equations (11). Different symbols and colors depict Ising phases N^z (green region) and N^y (yellow region) and the critical Luttinger liquid phase (purple region) according to the RG flow criteria summarized in Table I.

All figures and tables (11 total)

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Anyons in an exactly solved model and beyond
journal, January 2006

Kitaev, Alexei
Annals of Physics, Vol. 321, Issue 1
DOI: 10.1016/j.aop.2005.10.005

A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics
journal, January 1958

Dzyaloshinsky, I.
Journal of Physics and Chemistry of Solids, Vol. 4, Issue 4
DOI: 10.1016/0022-3697(58)90076-3

Electron spin resonance in a model $S = \frac{1}{2}$ chain antiferromagnet with a uniform Dzyaloshinskii-Moriya interaction
journal, October 2015

Smirnov, A. I.; Soldatov, T. A.; Povarov, K. Yu.
Physical Review B, Vol. 92, Issue 13
DOI: 10.1103/PhysRevB.92.134417

Correlation amplitude for the $S = \frac{1}{2}$ $XXZ$ spin chain in the critical region: Numerical renormalization-group study of an open chain
journal, July 1998

Hikihara, T.; Furusaki, A.
Physical Review B, Vol. 58, Issue 2
DOI: 10.1103/PhysRevB.58.R583

Modes of Magnetic Resonance in the Spin-Liquid Phase of ${Cs}_{2} {CuCl}_{4}$
journal, July 2011

Povarov, K. Yu.; Smirnov, A. I.; Starykh, O. A.
Physical Review Letters, Vol. 107, Issue 3
DOI: 10.1103/PhysRevLett.107.037204

Theory of spin-anisotropic electron-electron interactions in quasi-one-dimensional metals
journal, January 1988

Giamarchi, T.; Schulz, H. J.
Journal de Physique, Vol. 49, Issue 5
DOI: 10.1051/jphys:01988004905081900

Measuring the Dzyaloshinskii–Moriya interaction in a weak ferromagnet
journal, February 2014

Dmitrienko, V. E.; Ovchinnikova, E. N.; Collins, S. P.
Nature Physics, Vol. 10, Issue 3
DOI: 10.1038/nphys2859

Correlation amplitudes for the spin- $\frac{1}{2}$ $XXZ$ chain in a magnetic field
journal, February 2004

Hikihara, T.; Furusaki, A.
Physical Review B, Vol. 69, Issue 6
DOI: 10.1103/PhysRevB.69.064427

Interplay between symmetric exchange anisotropy, uniform Dzyaloshinskii-Moriya interaction, and magnetic fields in the phase diagram of quantum magnets and superconductors
journal, April 2010

Garate, Ion; Affleck, Ian
Physical Review B, Vol. 81, Issue 14
DOI: 10.1103/PhysRevB.81.144419

Spin-orbital effects in magnetized quantum wires and spin chains
journal, August 2008

Gangadharaiah, Suhas; Sun, Jianmin; Starykh, Oleg A.
Physical Review B, Vol. 78, Issue 5
DOI: 10.1103/PhysRevB.78.054436

Efficient Simulation of One-Dimensional Quantum Many-Body Systems
journal, July 2004

Vidal, Guifré
Physical Review Letters, Vol. 93, Issue 4
DOI: 10.1103/PhysRevLett.93.040502

Exact expectation values of local fields in the quantum sine-Gordon model
journal, June 1997

Lukyanov, Sergei; Zamolodchikov, Alexander
Nuclear Physics B, Vol. 493, Issue 3
DOI: 10.1016/S0550-3213(97)00123-5

The density-matrix renormalization group
journal, April 2005

Schollwöck, U.
Reviews of Modern Physics, Vol. 77, Issue 1
DOI: 10.1103/RevModPhys.77.259

Quantum spin chains with frustration due to Dzyaloshinskii-Moriya interactions
journal, November 2014

Hälg, M.; Lorenz, W. E. A.; Povarov, K. Yu.
Physical Review B, Vol. 90, Issue 17
DOI: 10.1103/PhysRevB.90.174413

Density-matrix algorithms for quantum renormalization groups
journal, October 1993

White, Steven R.
Physical Review B, Vol. 48, Issue 14
DOI: 10.1103/PhysRevB.48.10345

Phase diagram of the $spin - \frac{1}{2}$ triangular $J_{1} - J_{2}$ Heisenberg model on a three-leg cylinder
journal, June 2015

Saadatmand, S. N.; Powell, B. J.; McCulloch, I. P.
Physical Review B, Vol. 91, Issue 24
DOI: 10.1103/PhysRevB.91.245119

New directions in the pursuit of Majorana fermions in solid state systems
journal, June 2012

Alicea, Jason
Reports on Progress in Physics, Vol. 75, Issue 7
DOI: 10.1088/0034-4885/75/7/076501

Critical phenomena and renormalization-group theory
journal, October 2002

Pelissetto, Andrea; Vicari, Ettore
Physics Reports, Vol. 368, Issue 6
DOI: 10.1016/S0370-1573(02)00219-3

Anisotropic pyrochlores and the global phase diagram of the checkerboard antiferromagnet
journal, September 2005

Starykh, Oleg A.; Furusaki, Akira; Balents, Leon
Physical Review B, Vol. 72, Issue 9
DOI: 10.1103/PhysRevB.72.094416

Unpaired Majorana fermions in quantum wires
journal, October 2001

Kitaev, A. Yu
Physics-Uspekhi, Vol. 44, Issue 10S
DOI: 10.1070/1063-7869/44/10S/S29

Density matrix formulation for quantum renormalization groups
journal, November 1992

White, Steven R.
Physical Review Letters, Vol. 69, Issue 19
DOI: 10.1103/PhysRevLett.69.2863

Spin correlations in quantum wires
journal, April 2015

Sun, Chen; Pokrovsky, Valery L.
Physical Review B, Vol. 91, Issue 16
DOI: 10.1103/PhysRevB.91.161305

Spatially anisotropic Heisenberg kagome antiferromagnet
journal, November 2008

Schnyder, Andreas P.; Starykh, Oleg A.; Balents, Leon
Physical Review B, Vol. 78, Issue 17
DOI: 10.1103/PhysRevB.78.174420

Multiferroics: a magnetic twist for ferroelectricity
journal, January 2007

Cheong, Sang-Wook; Mostovoy, Maxim
Nature Materials, Vol. 6, Issue 1
DOI: 10.1038/nmat1804

Anisotropic Superexchange Interaction and Weak Ferromagnetism
journal, October 1960

Moriya, Tôru
Physical Review, Vol. 120, Issue 1
DOI: 10.1103/PhysRev.120.91

Gap generation in the $XXZ$ model in a transverse magnetic field
journal, April 2002

Dmitriev, D. V.; Krivnov, V. Ya.; Ovchinnikov, A. A.
Physical Review B, Vol. 65, Issue 17
DOI: 10.1103/PhysRevB.65.172409

Chiral Magnetic Soliton Lattice on a Chiral Helimagnet
journal, March 2012

Togawa, Y.; Koyama, T.; Takayanagi, K.
Physical Review Letters, Vol. 108, Issue 10
DOI: 10.1103/PhysRevLett.108.107202

Dimer correlation amplitudes and dimer excitation gap in spin- $\frac{1}{2}$ XXZ and Heisenberg chains
journal, October 2017

Hikihara, Toshiya; Furusaki, Akira; Lukyanov, Sergei
Physical Review B, Vol. 96, Issue 13
DOI: 10.1103/PhysRevB.96.134429

Phase diagram of weakly coupled Heisenberg spin chains subject to a uniform Dzyaloshinskii-Moriya interaction
journal, June 2017

Jin, Wen; Starykh, Oleg A.
Physical Review B, Vol. 95, Issue 21
DOI: 10.1103/PhysRevB.95.214404

Efficient Classical Simulation of Slightly Entangled Quantum Computations
journal, October 2003

Vidal, Guifré
Physical Review Letters, Vol. 91, Issue 14
DOI: 10.1103/PhysRevLett.91.147902

Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension
journal, February 2007

Vidal, G.
Physical Review Letters, Vol. 98, Issue 7
DOI: 10.1103/PhysRevLett.98.070201

Field-induced incommensurate-to-commensurate transition in ${Ba}_{2} {CuGe}_{2} O_{7}$
journal, February 1998

Zheludev, A.; Maslov, S.; Shirane, G.
Physical Review B, Vol. 57, Issue 5
DOI: 10.1103/PhysRevB.57.2968

New perspectives for Rashba spin–orbit coupling
journal, August 2015

Manchon, A.; Koo, H. C.; Nitta, J.
Nature Materials, Vol. 14, Issue 9
DOI: 10.1038/nmat4360

Efficient evaluation of high-order moments and cumulants in tensor network states
journal, September 2015

West, Colin G.; Garcia-Saez, Artur; Wei, Tzu-Chieh
Physical Review B, Vol. 92, Issue 11
DOI: 10.1103/PhysRevB.92.115103

Works referencing / citing this record:

Ineffectiveness of the Dzyaloshinskii–Moriya interaction in the dynamical quantum phase transition in the ITF model
journal, October 2018

Cheraghi, Hadi; Mahdavifar, Saeed
Journal of Physics: Condensed Matter, Vol. 30, Issue 42
DOI: 10.1088/1361-648x/aae1c5

Figures / Tables found in this record:

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

Similar Records in DOE PAGES and OSTI.GOV collections:

Coexistence of glassiness and canted antiferromagnetism in triangular quantum Heisenberg antiferromagnets with weak Dzyaloshinskii-Moriya interaction

Journal Article Girtu, M A ; Wynn, C M ; Fujita, W ; ... - Physical Review, B: Condensed Matter

We present magnetic studies of three triangular quantum Heisenberg antiferromagnets (TQHAF{close_quote}s) with weak additional Dzyaloshinskii-Moriya interaction, Cu{sub 2}(OH){sub 3}(C{sub m}H{sub 2m+1}COO), m=7, 9, and 11. Fits of the dc susceptibility data to high-temperature series expansions agree with high-temperature TQHAF behavior. At low temperatures the deviations from the TQHAF predictions suggest a canted antiferromagnetic type of ordering, while the strong peak in the second harmonic of the nonlinear ac susceptibility indicates the development of a spontaneous moment. The frequency dependence of the linear ac susceptibility and the irreversibility in the field-cooled/zero-field-cooled magnetization show that frustration is strong enough to cause glassiness.more »« less
https://doi.org/10.1103/PhysRevB.57.R11058
Quantum entanglement and quantum phase transition in the XY model with staggered Dzyaloshinskii-Moriya interaction

Journal Article Fuwu, Ma ; Shengxin, Liu ; Xiangmu, Kong - Physical Review. A

We study the quantum entanglement and quantum phase transition (QPT) of the anisotropic spin-1/2 XY model with staggered Dzyaloshinskii-Moriya (DM) interaction by means of the quantum renormalization group method. The scaling of coupling constants and the critical points of the system are obtained. It is found that when the number of renormalization group iterations tends to infinity, the system exhibit a QPT between the spin-fluid and Neel phases which correspond with two saturated values of the concurrence for a given value of the strength of DM interaction. The DM interaction can enhance the entanglement and influence the QPT of themore »« less
https://doi.org/10.1103/PHYSREVA.84.042302
Study of Ising antiferromagnet with Dzyaloshinskii-Moriya interaction

Journal Article Mondal, Kallol ; Kadolkar, Charudatt - AIP Conference Proceedings

We have studied the ground state phase diagram of the Ising model with DM interaction in 1D rings using linear spin wave theory. We have also computed the properties using exact diagonalization of finite rings of sizes up to 32. It is shown that the ground state has two phases, a gapped Neel order phase in the D < J limit and a gapless chiral phase in the D > J limit. The results are in good agreement between spin wave theory and exact diagonalization..
https://doi.org/10.1063/1.4946209
The XY model with Dzyaloshinskii-Moriya interaction

Journal Article D'Souza, Ransell - AIP Conference Proceedings

One can get spin-orbit interaction of the magnetic ions, besides the strong Heisenberg interaction, known as the Dzyaloshinskii-Moriya (DM) interaction. We show the effect of the DM interaction on the excitation spectrum. We also show here the magnetic Susceptibility and ferroelectric polarization of the system in a longitudinal magnetic field.
https://doi.org/10.1063/1.4873011
Potential Skyrmion Host Fe(IO3)3: Connecting Stereoactive Lone-Pair Electron Effects to the Dzyaloshinskii-Moriya Interaction

Journal Article Oyeka, Ebube E. ; Winiarski, Michał J. ; Błachowski, Artur ; ... - Chemistry of Materials

Magnetic skyrmions, which are topologically distinct magnetic spin textures, are gaining increased attention for their unique physical properties and potential applications in spintronic devices. Here we present a design strategy for skyrmion host candidates based on combinations of magnetic spin, asymmetric building units having stereoactive lone-pair electrons, and polar lattice symmetry. To demonstrate the viability of the proposed rational design principles, we successfully synthesized a Fe(IO₃)₃ polycrystalline sample and single crystals by using a new simplified low-temperature pathway, which is experimentally feasible for extending materials growth of transition metal iodates. Single crystal X-ray and powder synchrotron X-ray diffraction measurements demonstratedmore »« less
https://doi.org/10.1021/acs.chemmater.1c01163

Full Text Available

Similar Records

Title: Ising order in a magnetized Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya interaction

Abstract

Citation Formats

Figures / Tables:

Anyons in an exactly solved model and beyond journal, January 2006

A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics journal, January 1958

Electron spin resonance in a model S = 1 2 chain antiferromagnet with a uniform Dzyaloshinskii-Moriya interaction journal, October 2015

Correlation amplitude for the S = 1 2 XXZ spin chain in the critical region: Numerical renormalization-group study of an open chain journal, July 1998

Modes of Magnetic Resonance in the Spin-Liquid Phase of Cs 2 CuCl 4 journal, July 2011

Theory of spin-anisotropic electron-electron interactions in quasi-one-dimensional metals journal, January 1988

Measuring the Dzyaloshinskii–Moriya interaction in a weak ferromagnet journal, February 2014

Correlation amplitudes for the spin- 1 2 XXZ chain in a magnetic field journal, February 2004

Interplay between symmetric exchange anisotropy, uniform Dzyaloshinskii-Moriya interaction, and magnetic fields in the phase diagram of quantum magnets and superconductors journal, April 2010

Spin-orbital effects in magnetized quantum wires and spin chains journal, August 2008

Efficient Simulation of One-Dimensional Quantum Many-Body Systems journal, July 2004

Exact expectation values of local fields in the quantum sine-Gordon model journal, June 1997

The density-matrix renormalization group journal, April 2005

Quantum spin chains with frustration due to Dzyaloshinskii-Moriya interactions journal, November 2014

Density-matrix algorithms for quantum renormalization groups journal, October 1993

Phase diagram of the spin − 1 2 triangular J 1 − J 2 Heisenberg model on a three-leg cylinder journal, June 2015

New directions in the pursuit of Majorana fermions in solid state systems journal, June 2012

Critical phenomena and renormalization-group theory journal, October 2002

Anisotropic pyrochlores and the global phase diagram of the checkerboard antiferromagnet journal, September 2005

Unpaired Majorana fermions in quantum wires journal, October 2001

Density matrix formulation for quantum renormalization groups journal, November 1992

Spin correlations in quantum wires journal, April 2015

Spatially anisotropic Heisenberg kagome antiferromagnet journal, November 2008

Multiferroics: a magnetic twist for ferroelectricity journal, January 2007

Anisotropic Superexchange Interaction and Weak Ferromagnetism journal, October 1960

Gap generation in the XXZ model in a transverse magnetic field journal, April 2002

Chiral Magnetic Soliton Lattice on a Chiral Helimagnet journal, March 2012

Dimer correlation amplitudes and dimer excitation gap in spin- 1 2 XXZ and Heisenberg chains journal, October 2017

Phase diagram of weakly coupled Heisenberg spin chains subject to a uniform Dzyaloshinskii-Moriya interaction journal, June 2017

Efficient Classical Simulation of Slightly Entangled Quantum Computations journal, October 2003

Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension journal, February 2007

Field-induced incommensurate-to-commensurate transition in Ba 2 CuGe 2 O 7 journal, February 1998

New perspectives for Rashba spin–orbit coupling journal, August 2015

Efficient evaluation of high-order moments and cumulants in tensor network states journal, September 2015

Ineffectiveness of the Dzyaloshinskii–Moriya interaction in the dynamical quantum phase transition in the ITF model journal, October 2018

Anyons in an exactly solved model and beyond
journal, January 2006

A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics
journal, January 1958

Electron spin resonance in a model $S = \frac{1}{2}$ chain antiferromagnet with a uniform Dzyaloshinskii-Moriya interaction
journal, October 2015

Correlation amplitude for the $S = \frac{1}{2}$ $XXZ$ spin chain in the critical region: Numerical renormalization-group study of an open chain
journal, July 1998

Modes of Magnetic Resonance in the Spin-Liquid Phase of ${Cs}_{2} {CuCl}_{4}$
journal, July 2011

Theory of spin-anisotropic electron-electron interactions in quasi-one-dimensional metals
journal, January 1988

Measuring the Dzyaloshinskii–Moriya interaction in a weak ferromagnet
journal, February 2014

Correlation amplitudes for the spin- $\frac{1}{2}$ $XXZ$ chain in a magnetic field
journal, February 2004

Interplay between symmetric exchange anisotropy, uniform Dzyaloshinskii-Moriya interaction, and magnetic fields in the phase diagram of quantum magnets and superconductors
journal, April 2010

Spin-orbital effects in magnetized quantum wires and spin chains
journal, August 2008

Efficient Simulation of One-Dimensional Quantum Many-Body Systems
journal, July 2004

Exact expectation values of local fields in the quantum sine-Gordon model
journal, June 1997

The density-matrix renormalization group
journal, April 2005

Quantum spin chains with frustration due to Dzyaloshinskii-Moriya interactions
journal, November 2014

Density-matrix algorithms for quantum renormalization groups
journal, October 1993

Phase diagram of the $spin - \frac{1}{2}$ triangular $J_{1} - J_{2}$ Heisenberg model on a three-leg cylinder
journal, June 2015

New directions in the pursuit of Majorana fermions in solid state systems
journal, June 2012

Critical phenomena and renormalization-group theory
journal, October 2002

Anisotropic pyrochlores and the global phase diagram of the checkerboard antiferromagnet
journal, September 2005

Unpaired Majorana fermions in quantum wires
journal, October 2001

Density matrix formulation for quantum renormalization groups
journal, November 1992

Spin correlations in quantum wires
journal, April 2015

Spatially anisotropic Heisenberg kagome antiferromagnet
journal, November 2008

Multiferroics: a magnetic twist for ferroelectricity
journal, January 2007

Anisotropic Superexchange Interaction and Weak Ferromagnetism
journal, October 1960

Gap generation in the $XXZ$ model in a transverse magnetic field
journal, April 2002

Chiral Magnetic Soliton Lattice on a Chiral Helimagnet
journal, March 2012

Dimer correlation amplitudes and dimer excitation gap in spin- $\frac{1}{2}$ XXZ and Heisenberg chains
journal, October 2017

Phase diagram of weakly coupled Heisenberg spin chains subject to a uniform Dzyaloshinskii-Moriya interaction
journal, June 2017

Efficient Classical Simulation of Slightly Entangled Quantum Computations
journal, October 2003

Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension
journal, February 2007

Field-induced incommensurate-to-commensurate transition in ${Ba}_{2} {CuGe}_{2} O_{7}$
journal, February 1998

New perspectives for Rashba spin–orbit coupling
journal, August 2015

Efficient evaluation of high-order moments and cumulants in tensor network states
journal, September 2015

Ineffectiveness of the Dzyaloshinskii–Moriya interaction in the dynamical quantum phase transition in the ITF model
journal, October 2018