Hi
I'm trying to get the gap (between the Sz=0 sector and the Sz=1/2 i.e. spinon) for a spin-1/2 anti-ferromagnetic Hiesenberg chain for a finite system L=4. No eigenvalues are calculated in the output file when I perform sparse diagonalization on the below parameter file for getting the spinon eigenvalue:
MODEL="spin"; LATTICE="chain lattice"; LATTICE_LIBRARY="../lattices.xml" MODEL_LIBRARY="../models.xml" CONSERVED_QUANTUMNUMBERS="Sz"; local_S=1/2; J=1; {L=4; Sz_total=1/2;}
It seems only the sectors with Sz= {-1,0,+1} can be input to the Lanczos algorithm. Can somebody tell me what I am missing?
Thanks, Vipin
Hi,
On Fri, Jun 18, 2010 at 4:07 AM, Vipin Varma varma@th.physik.uni-bonn.de wrote:
I'm trying to get the gap (between the Sz=0 sector and the Sz=1/2 i.e. spinon) for a spin-1/2 anti-ferromagnetic Hiesenberg chain for a finite system L=4. No eigenvalues are calculated in the output file when I perform sparse diagonalization on the below parameter file for getting the spinon eigenvalue:
MODEL="spin"; LATTICE="chain lattice"; LATTICE_LIBRARY="../lattices.xml" MODEL_LIBRARY="../models.xml" CONSERVED_QUANTUMNUMBERS="Sz"; local_S=1/2; J=1; {L=4; Sz_total=1/2;}
It seems only the sectors with Sz= {-1,0,+1} can be input to the Lanczos algorithm. Can somebody tell me what I am missing?
When you calculate Heisenberg model on L=4 chain lattice, there will only be 5 sectors available. up=4, down=0 -> Sz_total=2 up=3, down=1 -> Sz_total=1 up=2, down=2 -> Sz_total=0 up=1, down=3 -> Sz_total=-1 up=0, down=4 -> Sz_total=-2
Note that if you increase one up spin, one down spin must be decreased, so \Delta Sz_total is always an integer.
Hi Ryo
Thanks for the reply; so I guess I should consider chains with odd number of sites (whether for spin-1/2 or spin-1 chains) to calculate the corresponding topological excitations. Is this correct?
Vipin
On Fri, 18 Jun 2010, Ryo IGARASHI wrote:
Hi,
On Fri, Jun 18, 2010 at 4:07 AM, Vipin Varma varma@th.physik.uni-bonn.de wrote:
I'm trying to get the gap (between the Sz=0 sector and the Sz=1/2 i.e. spinon) for a spin-1/2 anti-ferromagnetic Hiesenberg chain for a finite system L=4. No eigenvalues are calculated in the output file when I perform sparse diagonalization on the below parameter file for getting the spinon eigenvalue:
MODEL="spin"; LATTICE="chain lattice"; LATTICE_LIBRARY="../lattices.xml" MODEL_LIBRARY="../models.xml" CONSERVED_QUANTUMNUMBERS="Sz"; local_S=1/2; J=1; {L=4; Sz_total=1/2;}
It seems only the sectors with Sz= {-1,0,+1} can be input to the Lanczos algorithm. Can somebody tell me what I am missing?
When you calculate Heisenberg model on L=4 chain lattice, there will only be 5 sectors available. up=4, down=0 -> Sz_total=2 up=3, down=1 -> Sz_total=1 up=2, down=2 -> Sz_total=0 up=1, down=3 -> Sz_total=-1 up=0, down=4 -> Sz_total=-2
Note that if you increase one up spin, one down spin must be decreased, so \Delta Sz_total is always an integer.
-- Ryo IGARASHI, Ph.D. rigarash@hosi.phys.s.u-tokyo.ac.jp OpenPGP fingerprint: BAD9 71E3 28F3 8952 5640 6A53 EC79 A280 6A19 2319
Hi, Vipin,
On Fri, Jun 18, 2010 at 7:22 PM, Vipin Varma varma@th.physik.uni-bonn.de wrote:
Thanks for the reply; so I guess I should consider chains with odd number of sites (whether for spin-1/2 or spin-1 chains) to calculate the corresponding topological excitations. Is this correct?
No. You should think Sz_total=1 subspace as 2-spinon excited states. 2-spinon excited states are what experimentally observed (from e.g. neutron).
Best regards,
Hi Ryo
For spin-1/2 systems, I tried lattices from L=4,6,...22 and got a gap of 0.025 after extrapolation (between Sz=0 and Sz=1); can I consider this good enough to call it gapless, or do I need bigger lattices?
For spin-2, I tried lattices from L=4,6,8,10, and got a gap of 0.089; I guess the non-linear sigma model predicts S=2 system to have a gap of 0.071. Beyond L=12, it takes really long; what system size is considered "reasonable" for evalauting gap of spin-2?
Thanks, Vipin
On Sat, 19 Jun 2010, Ryo IGARASHI wrote:
Hi, Vipin,
On Fri, Jun 18, 2010 at 7:22 PM, Vipin Varma varma@th.physik.uni-bonn.de wrote:
Thanks for the reply; so I guess I should consider chains with odd number of sites (whether for spin-1/2 or spin-1 chains) to calculate the corresponding topological excitations. Is this correct?
No. You should think Sz_total=1 subspace as 2-spinon excited states. 2-spinon excited states are what experimentally observed (from e.g. neutron).
Best regards,
Ryo IGARASHI, Ph.D. rigarash@hosi.phys.s.u-tokyo.ac.jp OpenPGP fingerprint: BAD9 71E3 28F3 8952 5640 6A53 EC79 A280 6A19 2319
Hi, Vipin,
On Sat, Jun 19, 2010 at 12:22 AM, Vipin Varma varma@th.physik.uni-bonn.de wrote:
For spin-1/2 systems, I tried lattices from L=4,6,...22 and got a gap of 0.025 after extrapolation (between Sz=0 and Sz=1); can I consider this good enough to call it gapless, or do I need bigger lattices?
If you need longer chain, you may consider using DMRG or QMC[1]. You can also find these applications in ALPS.
For spin-2, I tried lattices from L=4,6,8,10, and got a gap of 0.089; I guess the non-linear sigma model predicts S=2 system to have a gap of 0.071. Beyond L=12, it takes really long; what system size is considered "reasonable" for evalauting gap of spin-2?
According to [1], spin 2 system have spin-spin correlation length of order L=50. I don't think L=12 is sufficient to evaluate the gap.
[1] S. Todo and K. Kato, Phys. Rev. Lett. 87, 047203 (2001).
See more papers available at http://alps.comp-phys.org/mediawiki/index.php/PapersTalks
Best regards,
comp-phys-alps-users@lists.phys.ethz.ch