Two questions about truncation error and entanglement entropy
Dear, M. Dolfi I am a freshman about DMRG. I have two questions : (1) How to get truncation error using mps_optim codes ? (2) How to get von Neumann entanglement entropy S(A) of a system A. Actually, I have obtained entanglement entropy data by setting MEASURE[Entropy]=1 using mps_optim. For a spin chain, we got the data number of entanglement entropy which seems the same as the number of 'bond' in chain. For example, to run a mps_optim of a spin chain with 32 sites , I will get 31 data in output of entropy. What meaning of such entanglement entropy data? How to get von Neumann entanglement entropy S(A) of a two dimension system A (Just like page 5 in paper Phys.Rev.B 64,024424(2012)) L.J.Meng Xiangtan University ------------------
Dear L.J.Meng, see below.
On Apr 8, 2016, at 9:01 AM, Forwordom <mljphy@qq.com> wrote:
Dear, M. Dolfi
I am a freshman about DMRG. I have two questions : (1) How to get truncation error using mps_optim codes ?
An example is given in the tutorial files that you find in /tutorials/mps-01-optim. iterations = pyalps.loadIterationMeasurements(pyalps.getResultFiles(prefix='parm_spin_one_half’), what=['TruncatedWeight']) truncation_iteration = pyalps.collectXY(pyalps.flatten(iterations), 'iteration', 'TruncatedWeight')
(2) How to get von Neumann entanglement entropy S(A) of a system A. Actually, I have obtained entanglement entropy data by setting MEASURE[Entropy]=1 using mps_optim. For a spin chain, we got the data number of entanglement entropy which seems the same as the number of 'bond' in chain. For example, to run a mps_optim of a spin chain with 32 sites , I will get 31 data in output of entropy. What meaning of such entanglement entropy data? How to get von Neumann entanglement entropy S(A) of a two dimension system A (Just like page 5 in paper Phys.Rev.B 64,024424(2012))
The Entropy measurement is the von Neumann entanglement entropy, computed on each bond. In the paper that you highlight, I think the authors optimized one MPS for each L_y, then compute the von Neumann entanglement entropy on the central MPS bond. Basically on a L_x * L_y = 20 * 4 system, on the bond between the MPS site 39 and 40. (when counting from 0) Best regards, Michele -- ETH Zurich Michele Dolfi Institute for Theoretical Physics HIT G 32.4 Wolfgang-Pauli-Str. 27 8093 Zurich Switzerland dolfim@phys.ethz.ch www.itp.phys.ethz.ch +41 44 633 78 56 phone +41 44 633 11 15 fax
Additionally you can also look at the tutorials by B. Bauer: https://alps.comp-phys.org/mediawiki/index.php/ALPS_2_Tutorials:Trieste -- ETH Zurich Michele Dolfi Institute for Theoretical Physics HIT G 32.4 Wolfgang-Pauli-Str. 27 8093 Zurich Switzerland dolfim@phys.ethz.ch www.itp.phys.ethz.ch +41 44 633 78 56 phone +41 44 633 11 15 fax
On Apr 8, 2016, at 9:51 AM, Michele Dolfi <dolfim@phys.ethz.ch> wrote:
Dear L.J.Meng, see below.
On Apr 8, 2016, at 9:01 AM, Forwordom <mljphy@qq.com <mailto:mljphy@qq.com>> wrote:
Dear, M. Dolfi
I am a freshman about DMRG. I have two questions : (1) How to get truncation error using mps_optim codes ?
An example is given in the tutorial files that you find in /tutorials/mps-01-optim. iterations = pyalps.loadIterationMeasurements(pyalps.getResultFiles(prefix='parm_spin_one_half’), what=['TruncatedWeight']) truncation_iteration = pyalps.collectXY(pyalps.flatten(iterations), 'iteration', 'TruncatedWeight')
(2) How to get von Neumann entanglement entropy S(A) of a system A. Actually, I have obtained entanglement entropy data by setting MEASURE[Entropy]=1 using mps_optim. For a spin chain, we got the data number of entanglement entropy which seems the same as the number of 'bond' in chain. For example, to run a mps_optim of a spin chain with 32 sites , I will get 31 data in output of entropy. What meaning of such entanglement entropy data? How to get von Neumann entanglement entropy S(A) of a two dimension system A (Just like page 5 in paper Phys.Rev.B 64,024424(2012))
The Entropy measurement is the von Neumann entanglement entropy, computed on each bond.
In the paper that you highlight, I think the authors optimized one MPS for each L_y, then compute the von Neumann entanglement entropy on the central MPS bond. Basically on a L_x * L_y = 20 * 4 system, on the bond between the MPS site 39 and 40. (when counting from 0)
Best regards, Michele
-- ETH Zurich Michele Dolfi Institute for Theoretical Physics HIT G 32.4 Wolfgang-Pauli-Str. 27 8093 Zurich Switzerland
dolfim@phys.ethz.ch <mailto:dolfim@phys.ethz.ch> www.itp.phys.ethz.ch <http://www.itp.phys.ethz.ch/>
+41 44 633 78 56 phone +41 44 633 11 15 fax
participants (2)
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Forwordom
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Michele Dolfi